Optical filter and imaging apparatus

ABSTRACT

An optical filter (1a) includes a light-absorbing layer (10). The light-absorbing layer absorbs light in at least a portion of the near-infrared region. When light with a wavelength of 300 nm to 1200 nm is incident on the optical filter (1a) at incident angles of 0°, 30°, and 40°, the optical filter (1a) satisfies given transmittance requirements. IEθ1/θ2λ1 to λ2, IAEθ1/θ2λ1 to λ2, and ISEθ1/θ2λ1 to λ2 defined by the following equations (1) to (3) for two incident angles θ1° and θ2° (θ1&lt;θ2) selected from 0°, 30°, and 40° satisfy given requirements in a given domain of a wavelength λ.

TECHNICAL FIELD

The present invention relates to an optical filter and imaging apparatus.

BACKGROUND ART

Imaging apparatuses including an optical filter such as a near-infrared cut filter are conventionally known. For example, Patent Literature 1 describes a near-infrared cut filter including a laminated sheet having a near-infrared-absorber-including resin layer provided on at least one side of a glass sheet substrate. For example, this near-infrared cut filter has a dielectric multilayer film provided on at least one side of the laminated sheet. For this near-infrared cut filter, the absolute value |Ya−Yb| of the difference between a wavelength value (Ya) and a wavelength value (Yb) is less than 15 nm. The wavelength value (Ya) is a value of a wavelength which lies in the wavelength range of 560 to 800 nm and at which the transmittance measured in the direction perpendicular to the near-infrared cut filter is 50%. The wavelength value (Yb) is a value of a wavelength which lies in the wavelength range of 560 to 800 nm and at which the transmittance measured at an incident angle of 30° to the near-infrared cut filter is 50%. As just described, the angle dependence of the transmission characteristics of the near-infrared cut filter according to Patent Literature 1 is adjusted to be small.

Patent Literature 2 describes a near-infrared cut filter including a near-infrared-absorbing glass substrate, near-infrared-absorbing layer, and dielectric multilayer film. The near-infrared-absorbing layer includes a near-infrared-absorbing dye and transparent resin. Patent Literature 2 describes a solid-state imaging apparatus including this near-infrared cut filter and a solid-state imaging device. According to Patent Literature 2, the influence of the angle dependence which dielectric multilayer films inherently have and which is an incident-angle-dependent shift of a shielding wavelength can be almost completely eliminated by laminating the near-infrared-absorbing glass substrate and near-infrared-absorbing layer. For example, in Patent Literature 2, a transmittance (T₀) at an incident angle of 0° and a transmittance (T₃₀) at an incident angle of 30° are measured for the near-infrared cut filter.

Patent Literatures 3 and 4 each describe an infrared cut filter including a dielectric substrate, an infrared-reflecting layer, and an infrared-absorbing layer. The infrared-reflecting layer is formed of a dielectric multilayer film. The infrared-absorbing layer includes an infrared-absorbing dye. Patent Literatures 3 and 4 each describe an imaging apparatus including this infrared cut filter. Patent Literatures 3 and 4 each describe transmittance spectra shown by the infrared cut filter for light incident at incident angles of 0°, 25°, and 35°.

Patent Literature 5 describes a near-infrared cut filter including an absorbing layer and a reflecting layer and satisfying given requirements. For example, the difference |T₀₍₆₀₀₋₇₂₅₎−T₃₀₍₆₀₀₋₇₂₅₎| between an integral T₀₍₆₀₀₋₇₂₅₎ of transmittances of light with wavelengths of 600 to 725 nm in a spectral transmittance curve shown by this near-infrared cut filter at an incident angle of 0° and an integral T₃₀₍₆₀₀₋₇₂₅₎ of transmittances of light with wavelengths of 600 to 725 nm in a spectral transmittance curve shown thereby at an incident angle of 30° is 3% nm or less. Patent Literature 5 also describes an imaging apparatus including this near-infrared cut filter.

CITATION LIST Patent Literature

-   -   Patent Literature 1: JP 2012-103340 A     -   Patent Literature 2: WO 2014/030628 A1     -   Patent Literature 3: US 2014/0300956 A1     -   Patent Literature 4: US 2014/0063597 A1     -   Patent Literature 5: JP 6119920 B2

SUMMARY OF INVENTION Technical Problem

The above patent literatures fail to specifically discuss the characteristics which would be exhibited by the optical filters when light is incident on the optical filters at an incident angle larger than 35 (e.g., 40°). Moreover, the above patent literatures fail to discuss compatibility with the characteristics of a color filter used in imaging apparatuses such as cameras. Therefore, the present invention provides an optical filter that is likely to be compatible with the characteristics of a color filter used in an imaging apparatus even when the incident angle of light is larger and that exhibits characteristics advantageous to prevent uneven coloring of an image generated by an imaging apparatus. The present invention also provides an imaging apparatus including this optical filter.

Solution to Problem

The present invention is an optical filter, including

-   -   a light-absorbing layer that includes a light absorber absorbing         light in at least a portion of the near-infrared region, wherein     -   when light with a wavelength of 300 nm to 1200 nm is incident on         the optical filter at incident angles of 0°, 30°, and 40°, the         optical filter satisfies the following requirements:     -   (i) the spectral transmittance at a wavelength of 700 nm is 3%         or less;     -   (ii) the spectral transmittance at a wavelength of 715 nm is 1%         or less;     -   (iii) the spectral transmittance at a wavelength of 1100 nm is         7.5% or less;     -   (iv) the average transmittance in the wavelength range of 700 nm         to 800 nm is 1% or less;     -   (v) the average transmittance in the wavelength range of 500 nm         to 600 nm is 85% or more;     -   (vi) the spectral transmittance at a wavelength of 400 nm is 45%         or less; and     -   (vii) the spectral transmittance at a wavelength of 450 nm is         80% or more, and     -   in the case where the spectral transmittance of the optical         filter at a wavelength λ and an incident angle θ° is expressed         by T_(θ)(λ),     -   where the minimum and the maximum in a domain of the wavelength         λ are respectively expressed by λ1 [nm] and λ2 [nm], and     -   where the wavelength λ is expressed by λ(n)=(Δλ×n+λ1) [nm]         (Δλ=1) as a function of an integer n of 0 or more,     -   IE_(θ1/θ2) ^(λ1 to λ2), IAE_(θ1/θ2) ^(λ1 to λ2), and ISE_(θ1/θ2)         ^(λ1 to λ2) defined by the following equations (1) to (3) for         two incident angles θ1° and θ2° (θ1<θ2) selected from 0°, 30°,         and 40° satisfy requirements shown in the following Tables (I),         (II), (III), and (IV) in a domain of the wavelength λ where         λ1=350 and λ2=800, a domain of the wavelength λ where λ1=380 and         λ2=530, a domain of the wavelength λ where λ1=450 and λ2=650,         and a domain of the wavelength λ where λ1=530 and λ2=750.

$\begin{matrix} {{IE}_{\theta\;{1/\theta}\; 2}^{\lambda\; 1\mspace{14mu}{to}\mspace{14mu}\lambda\; 2} = {\sum\limits_{n = 0}^{{{({{\lambda\; 2} - {\lambda\; 1}})}/\Delta}\;\lambda}{\left\{ {{T_{\theta\; 1}\left( {\lambda(n)} \right)} - {T_{\theta\; 2}\left( {\lambda(n)} \right)}} \right\} \times \Delta\;\lambda}}} & (1) \\ {{IAE}_{\theta\;{1/\theta}\; 2}^{\lambda\; 1\mspace{14mu}{to}\mspace{14mu}\lambda\; 2} = {\sum\limits_{n = 0}^{{{({{\lambda\; 2} - {\lambda\; 1}})}/\Delta}\;\lambda}{{{{T_{\theta\; 1}\left( {\lambda(n)} \right)} - {T_{\theta\; 2}\left( {\lambda(n)} \right)}}} \times \Delta\;\lambda}}} & (2) \\ {{ISE}_{\theta\;{1/\theta}\; 2}^{\lambda\; 1\mspace{14mu}{to}\mspace{14mu}\lambda\; 2} = {\sum\limits_{n = 0}^{{{({{\lambda\; 2} - {\lambda\; 1}})}/\Delta}\;\lambda}{\left\{ {{T_{\theta\; 1}\left( {\lambda(n)} \right)} - {T_{\theta\; 2}\left( {\lambda(n)} \right)}} \right\}^{2} \times \Delta\;\lambda}}} & (3) \end{matrix}$

TABLE 1 IE_(0/30) ^(350 to 800) IE_(0/40) ^(350 to 800) IE_(30/40) ^(350 to 800) −10 to 10 −14 to 14 −7 to 7 IAE_(0/30) ^(350 to 800) IAE_(0/40) ^(350 to 800) IAE_(30/40) ^(350 to 800) 0 to 7 0 to 10 0 to 7 ISE_(0/30) ^(350 to 800) ISE_(0/40) ^(350 to 800) ISE_(30/40) ^(350 to 800) 0 to 0.7 0 to 1 0 to 0.7

TABLE 2 IE_(0/30) ^(380 to 530) IE_(0/40) ^(380 to 530) IE_(30/40) ^(380 to 530) −7 to 7 −10 to 10 −5 to 5 IAE_(0/30) ^(380 to 530) IAE_(0/40) ^(380 to 530) IAE_(30/40) ^(380 to 530) 0 to 7 0 to 10 0 to 5 ISE_(0/30) ^(380 to 530) ISE_(0/40) ^(380 to 530) ISE_(30/40) ^(380 to 530) 0 to 0.7 0 to 1 0 to 0.5

TABLE 3 IE_(0/30) ^(450 to 650) IE_(0/40) ^(450 to 650) IE_(30/40) ^(450 to 650) −7 to 7 −10 to 10 −5 to 5 IAE_(0/30) ^(450 to 650) IAE_(0/40) ^(450 to 650) IAE_(30/40) ^(450 to 650) 0~7 0~10 0~5 ISE_(0/30) ^(450 to 650) ISE_(0/40) ^(450 to 650) ISE_(30/40) ^(450 to 650) 0~0.7 0~1 0~0.5

TABLE 4 IE_(0/30) ^(530 to 750) IE_(0/40) ^(530 to 750) IE_(30/40) ^(530 to 750) −7 to 7 −10 to 10 −5 to 5 IAE_(0/30) ^(530 to 750) IAE_(0/40) ^(530 to 750) IAE_(30/40) ^(530 to 750) 0 to 7 0 to 10 0 to 5 ISE_(0/30) ^(530 to 750) ISE_(0/40) ^(530 to 750) ISE_(30/40) ^(530 to 750) 0 to 0.7 0 to 1 0 to 0.5

The present invention also provides an imaging apparatus, including

-   -   a lens system;     -   an imaging device that receives light having been transmitted         through the lens system;     -   a color filter that is disposed ahead of the imaging device and         is a filter of three colors, R (red), G (green), and B (blue);         and     -   the above optical filter that is disposed ahead of the color         filter.

Advantageous Effects of Invention

Even when the incident angle of light is larger, the above optical filter can appropriately shield against unnecessary light without reducing brightness. Additionally, the above optical filter is likely to be compatible with the characteristics of a color filter used in an imaging apparatus such as a camera even when the incident angle of light is larger and exhibits characteristics advantageous to prevent uneven coloring of an image generated by an imaging apparatus. Moreover, an image generated by the above imaging apparatus of the present invention is unlikely to be colored unevenly even when the incident angle of light is larger.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1A is a cross-sectional view of an example of an optical filter of the present invention.

FIG. 1B is a cross-sectional view of another example of the optical filter of the present invention.

FIG. 1C is a cross-sectional view of yet another example of the optical filter of the present invention.

FIG. 1D is a cross-sectional view of yet another example of the optical filter of the present invention.

FIG. 1E is a cross-sectional view of yet another example of the optical filter of the present invention.

FIG. 1F is a cross-sectional view of yet another example of the optical filter of the present invention.

FIG. 2 is a cross-sectional view showing an example of a camera of the present invention.

FIG. 3A shows a transmittance spectrum of an intermediate product of an optical filter according to Example 1.

FIG. 3B shows a transmittance spectrum of another intermediate product of the optical filter according to Example 1.

FIG. 3C shows a transmittance spectrum of a laminate according to Reference Example 1.

FIG. 3D shows transmittance spectra of a laminate according to Reference Example 2.

FIG. 3E shows transmittance spectra of the optical filter according to Example 1.

FIG. 4A is a graph showing differences between spectral transmittances of the optical filter according to Example 1 at different incident angles.

FIG. 4B is a graph showing the absolute values of the differences between the spectral transmittances of the optical filter according to Example 1 at different incident angles.

FIG. 4C is a graph showing the square values of the differences between the spectral transmittances of the optical filter according to Example 1 at different incident angles.

FIG. 5A shows a transmittance spectrum of a laminate according to Reference Example 3.

FIG. 5B shows transmittance spectra of an optical filter according to Example 2.

FIG. 6A is a graph showing differences between spectral transmittances of the optical filter according to Example 2 at different incident angles.

FIG. 6B is a graph showing the absolute values of the differences between the spectral transmittances of the optical filter according to Example 2 at different incident angles.

FIG. 6C is a graph showing the square values of the differences between the spectral transmittances of the optical filter according to Example 2 at different incident angles.

FIG. 7A shows a transmittance spectrum of an intermediate product of an optical filter according to Example 3.

FIG. 7B shows transmittance spectra of the optical filter according to Example 3.

FIG. 8A is a graph showing differences between spectral transmittances of the optical filter according to Example 3 at different incident angles.

FIG. 8B is a graph showing the absolute values of the differences between the spectral transmittances of the optical filter according to Example 3 at different incident angles.

FIG. 8C is a graph showing the square values of the differences between the spectral transmittances of the optical filter according to Example 3 at different incident angles.

FIG. 9A shows transmittance spectra of a laminate according to Reference Example 4.

FIG. 9B shows transmittance spectra of an optical filter according to Example 4.

FIG. 10A is a graph showing differences between spectral transmittances of the optical filter according to Example 4 at different incident angles.

FIG. 10B is a graph showing the absolute values of the differences between the spectral transmittances of the optical filter according to Example 4 at different incident angles.

FIG. 10C is a graph showing the square values of the differences between the spectral transmittances of the optical filter according to Example 4 at different incident angles.

FIG. 11 shows transmittance spectra of an optical filter according to Example 5.

FIG. 12A is a graph showing differences between spectral transmittances of the optical filter according to Example 5 at different incident angles.

FIG. 12B is a graph showing the absolute values of the differences between the spectral transmittances of the optical filter according to Example 5 at different incident angles.

FIG. 12C is a graph showing the square values of the differences between the spectral transmittances of the optical filter according to Example 5 at different incident angles.

FIG. 13A shows a transmittance spectrum of an intermediate product of an optical filter according to Example 6.

FIG. 13B shows transmittance spectra of the optical filter according to Example 6.

FIG. 14A is a graph showing differences between spectral transmittances of the optical filter according to Example 6 at different incident angles.

FIG. 14B is a graph showing the absolute values of the differences between the spectral transmittances of the optical filter according to Example 6 at different incident angles.

FIG. 14C is a graph showing the square values of the differences between the spectral transmittances of the optical filter according to Example 6 at different incident angles.

FIG. 15A shows transmittance spectra of an intermediate product of an optical filter according to Comparative Example 1.

FIG. 15B shows a transmittance spectrum of a laminate according to Reference Example 5.

FIG. 15C shows transmittance spectra of the optical filter according to Comparative Example 1.

FIG. 16A is a graph showing differences between spectral transmittances of the optical filter according to Comparative Example 1 at different incident angles.

FIG. 16B is a graph showing the absolute values of the differences between the spectral transmittances of the optical filter according to Comparative Example 1 at different incident angles.

FIG. 16C is a graph showing the square values of the differences between the spectral transmittances of the optical filter according to Comparative Example 1 at different incident angles.

FIG. 17A shows a transmittance spectrum of an infrared-absorbing glass substrate of an optical filter according to Comparative Example 2.

FIG. 17B shows transmittance spectra of a laminate according to Reference Example 6.

FIG. 17C shows a transmittance spectrum of a laminate according to Reference Example 7.

FIG. 17D shows transmittance spectra of the optical filter according to Comparative Example 2.

FIG. 18A is a graph showing differences between spectral transmittances of the optical filter according to Comparative Example 2 at different incident angles.

FIG. 18B is a graph showing the absolute values of the differences between the spectral transmittances of the optical filter according to Comparative Example 2 at different incident angles.

FIG. 18C is a graph showing the square values of the differences between the spectral transmittances of the optical filter according to Comparative Example 2 at different incident angles.

DESCRIPTION OF EMBODIMENTS

Hereinafter, embodiments of the present invention will be described with reference to the drawings. The following description is directed to some examples of the present invention, and the present invention is not limited by these examples.

The present inventors have invented the optical filter according to the present invention based on new findings obtained from the following studies of optical filters.

An optical filter shielding against unnecessary light other than visible light is disposed in an imaging apparatus or a camera module mounted in a personal digital assistant such as a smartphone. The use of an optical filter including a light-absorbing layer has been discussed to shield against unnecessary light. Like the optical filters described in Patent Literatures 1 to 5, many optical filters including a light-absorbing layer further include a reflecting film composed of a dielectric multilayer film.

Interference of light reflecting on the front and back surfaces of each layer of a reflecting film composed of a dielectric multilayer film determines a wavelength band of transmitted light and a wavelength band of reflected light. Light can be incident on an optical filter at various incident angles. The optical path length in the reflecting film included in an optical filter changes depending on the incident angle of light incident on the optical filter. As a result, the wavelength bands of transmitted light and reflected light shift to the short wavelength side. Therefore, it is conceivable that in order not to greatly vary the transmittance characteristics of the optical filter depending on the incident angle of light, the boundary between a wavelength band of light to be blocked and a wavelength band of light to be transmitted is determined by a wavelength band of light absorption, and a wavelength band of light to be reflected by the dielectric multilayer film is separated apart from the wavelength band of light to be transmitted.

In Patent Literatures 1 and 2, the transmission characteristics of the near-infrared cut filters for light incident at incident angles of 0° and 30° are evaluated. In Patent Literatures 3 and 4, transmittance spectra shown by the infrared cut filters for light incident at incident angles of 0°, 25°, and 35° are evaluated. In recent years, camera modules mounted in personal digital assistants such as smartphones have been expected to achieve a wider angle of view and a much lower profile. Therefore, it is desirable that the wavelength band and amount of light transmitted through optical filters be unlikely to vary even when the incident angle of light is larger (e.g., 40°).

When light is incident on an optical filter including a reflecting film composed of a dielectric multilayer film at a large incident angle, the reflectance of light can locally increase in a wavelength band of light reflection of which should be reduced to achieve a high transmittance. As a result, the optical filter involves a defect called a ripple, i.e., a local decrease in transmittance. For example, even an optical filter designed not to produce a ripple upon incidence of light at an incident angle of 0° to 30° tends to produce a ripple when the incident angle of light is increased to 40°.

A measure has not yet been established for comprehensive evaluation of the effects arising from occurrence of a ripple and from an incident-angle-dependent shift of the boundary between a wavelength band of transmitted light and a wavelength band of blocked light. According to the technique described in Patent Literature 5, the boundary between the wavelength band of visible light which is expected to be transmitted and the wavelength band of near-infrared light which is expected to be reflected or absorbed is stable with respect to a variation in incident angle of light. However, the technique described in Patent Literature 5 has room for improvement in view of occurrence of a ripple and an incident-angle-dependent shift of the boundary between the wavelength band of visible light and the wavelength band of ultraviolet light.

R, G, and B segments of a color filter each correspond to a pixel of an image sensor included in an imaging apparatus, and the amount of light detected by each pixel of the sensor correlates with a product of a spectral transmittance of an optical filter shielding against unnecessary light and a spectral transmittance of each segment of the color filter. Therefore, optical filters desirably have characteristics compatible with the characteristics of a color filter used in an imaging apparatus.

Under these circumstances, the present inventors made intensive studies to discover an optical filter that can appropriately shield against unnecessary light without reducing brightness even when the incident angle of light is larger and that is likely to be compatible with the characteristics of a color filter used in an imaging apparatus even when the incident angle of light is larger. Additionally, the present inventors made intensive studies to discover an optical filter that exhibits characteristics advantageous to prevent uneven coloring of an image generated by an imaging apparatus even when the incident angle of light is larger. As a result, the present inventors have invented the optical filter according to the present invention.

Herein, the term “spectral transmittance” refers to a transmittance obtained when light with a given wavelength is incident on an object such as a specimen and the term “average transmittance” refers to an average of spectral transmittances in a given wavelength range. Additionally, the term “transmittance spectrum” herein refers to one in which spectral transmittances at wavelengths in a given wavelength range are arranged in the wavelength order.

Herein, the term “IR cut-off wavelength” refers to a wavelength which is determined by incidence of light with a wavelength of 300 nm to 1200 nm on the optical filter at a given incident angle, which lies in the wavelength range of 600 nm or more, and at which the spectral transmittance is 50%. The term “UV cut-off wavelength” refers to a wavelength which is determined by incidence of light with a wavelength of 300 nm to 1200 nm on the optical filter at a given incident angle, which lies in the wavelength range of 450 nm or less, and at which the spectral transmittance is 50%.

As shown in FIG. 1A, the optical filter 1 a includes a light-absorbing layer 10. The light-absorbing layer 10 includes a light absorber. The light absorber absorbs light in at least a portion of the near-infrared region. When light with a wavelength of 300 nm to 1200 nm is incident on the optical filter 1 a at incident angles of 0°, 30°, and 40°, the optical filter 1 a satisfies the following requirements:

-   -   (i) the spectral transmittance at a wavelength of 700 nm is 3%         or less;     -   (ii) the spectral transmittance at a wavelength of 715 nm is 1%         or less;     -   (iii) the spectral transmittance at a wavelength of 1100 nm is         7.5% or less;     -   (iv) the average transmittance in the wavelength range of 700 nm         to 800 nm is 1% or less;     -   (v) the average transmittance in the wavelength range of 500 nm         to 600 nm is 85% or more;     -   (vi) the spectral transmittance at a wavelength of 400 nm is 45%         or less; and     -   (vii) the spectral transmittance at a wavelength of 450 nm is         80% or more.

Since the optical filter 1 a satisfies the above requirements (i) to (vii), the optical filter 1 a incorporated in a wide-angle-lens-equipped camera module or imaging apparatus can shield against unnecessary light without reducing brightness.

The spectral transmittance of the optical filter 1 a at a wavelength λ and an incident angle θ° of light is expressed by T_(θ)(λ). The minimum and the maximum in a domain of the wavelength λ are respectively expressed by λ1 [nm] and λ2 [nm]. The wavelength λ is expressed by λ(n)=(Δλ×n+λ1) [nm] (Δλ=1) as a function of an integer n of 0 or more. The value of Δλ is a positive constant. Herein, Δλ=1. That is, λ(n) is defined at 1-nm intervals. When Δλ is a positive constant other than 1, the spectral transmittance T_(θ)(λ) based on λ(n) can be determined by linear interpolation. For the optical filter 1 a, IE_(θ1θ2) ^(λ1 to λ2), IAE_(θ1/θ2) ^(λ1 to λ2), and ISE_(θ1/θ2) ^(λ1 to λ2) satisfy requirements shown in the following Tables (I), (II), (III), and (V). IE_(θ1/θ2) ^(λ1 to λ2), IAE_(θ1/θ2) ^(λ1 to λ2), and ISE_(θ1/θ2) ^(λ1 to λ2) are defined by the following equations (1) to (3) for two incident angles θ1° and θ2° (θ1<θ2) selected from 0°, 30°, and 40° in a domain of the wavelength λ where λ1=350 and λ2=800, a domain of the wavelength λ where λ1=380 and λ2=530, a domain of the wavelength λ where λ1=450 and λ2=650, and a domain of the wavelength λ where λ1=530 and λ2=750.

$\begin{matrix} {{IE}_{\theta\;{1/\theta}\; 2}^{\lambda\; 1\mspace{14mu}{to}\mspace{14mu}\lambda\; 2} = {\sum\limits_{n = 0}^{{{({{\lambda\; 2} - {\lambda\; 1}})}/\Delta}\;\lambda}{\left\{ {{T_{\theta\; 1}\left( {\lambda(n)} \right)} - {T_{\theta\; 2}\left( {\lambda(n)} \right)}} \right\} \times \Delta\;\lambda}}} & (1) \\ {{IAE}_{\theta\;{1/\theta}\; 2}^{\lambda\; 1\mspace{14mu}{to}\mspace{14mu}\lambda\; 2} = {\sum\limits_{n = 0}^{{{({{\lambda\; 2} - {\lambda\; 1}})}/\Delta}\;\lambda}{{{{T_{\theta\; 1}\left( {\lambda(n)} \right)} - {T_{\theta\; 2}\left( {\lambda(n)} \right)}}} \times \Delta\;\lambda}}} & (2) \\ {{ISE}_{\theta\;{1/\theta}\; 2}^{\lambda\; 1\mspace{14mu}{to}\mspace{14mu}\lambda\; 2} = {\sum\limits_{n = 0}^{{{({{\lambda\; 2} - {\lambda\; 1}})}/\Delta}\;\lambda}{\left\{ {{T_{\theta\; 1}\left( {\lambda(n)} \right)} - {T_{\theta\; 2}\left( {\lambda(n)} \right)}} \right\}^{2} \times \Delta\;\lambda}}} & (3) \end{matrix}$

TABLE 5 IE_(0/30) ^(350 to 800) IE_(0/40) ^(350 to 800) IE_(30/40) ^(350 to 800) −10 to 10 −14 to 14 −7 to 7 IAE_(0/30) ^(350 to 800) IAE_(0/40) ^(350 to 800) IAE_(30/40) ^(350 to 800) 0 to 7 0 to 10 0 to 7 ISE_(0/30) ^(350 to 800) ISE_(0/40) ^(350 to 800) ISE_(30/40) ^(350 to 800) 0 to 0.7 0 to 1 0 to 0.7

TABLE 6 IE_(0/30) ^(380 to 530) IE_(0/40) ^(380 to 530) IE_(30/40) ^(380 to 530) −7 to 7 −10 to 10 −5 to 5 IAE_(0/30) ^(380 to 530) IAE_(0/40) ^(380 to 530) IAE_(30/40) ^(380 to 530) 0 to 7 0 to 10 0 to 5 ISE_(0/30) ^(380 to 530) ISE_(0/40) ^(380 to 530) ISE_(30/40) ^(380 to 530) 0 to 0.7 0 to 1 0 to 0.5

TABLE 7 IE_(0/30) ^(450 to 650) IE_(0/40) ^(450 to 650) IE_(30/40) ^(450 to 650) −7 to 7 −10 to 10 −5 to 5 IAE_(0/30) ^(450 to 650) IAE_(0/40) ^(450 to 650) IAE_(30/40) ^(450 to 650) 0 to 7 0 to 10 0 to 5 ISE_(0/30) ^(450 to 650) ISE_(0/40) ^(450 to 650) ISE_(30/40) ^(450 to 650) 0 to 0.7 0 to 1 0 to 0.5

TABLE 8 IE_(0/30) ^(530 to 750) IE_(0/40) ^(530 to 750) IE_(30/40) ^(530 to 750) −7 to 7 −10 to 10 −5 to 5 IAE_(0/30) ^(530 to 750) IAE_(0/40) ^(530 to 750) IAE_(30/40) ^(530 to 750) 0 to 7 0 to 10 0 to 5 ISE_(0/30) ^(530 to 750) ISE_(0/40) ^(530 to 750) ISE_(30/40) ^(530 to 750) 0 to 0.7 0 to 1 0 to 0.5

A chief ray is incident on the center of an imaging device of an imaging apparatus such as a camera at an incident angle of nearly 0° while incident on the peripheral portion of the imaging device at a large incident angle. When an optical filter that shows a change in the form of a spectral sensitivity curve or transmittance spectrum depending on the incident angle of light is mounted in an imaging apparatus, color of an image generated by the imaging apparatus can be changed at the time of printing or displaying the image. Therefore, when an image taken by an imaging apparatus is displayed or printed, an object expected to be colored with one color may gradually discolor from the center toward the peripheral portion, and the discoloration may be recognized as color unevenness. Compared to image regions affected by variations in incident angle of light from 0° to 40° and from 0° to 30°, an image region affected by a variation in incident angle of light from 30° to 40° is narrow. Color unevenness is more easily recognized in the latter region. Therefore, when the shape of a spectral transmittance curve of an optical filter changes little depending on the variation in incident angle of light incident on the optical filter, uneven coloring of an image generated by a camera can be prevented. Since the optical filter 1 a satisfies the requirements shown in Tables (I) to (V), the shape of its spectral transmittance curve changes little depending on the variation in incident angle of light. When an imaging apparatus includes the optical filter 1 a as just described, uneven coloring of an image generated by an imaging apparatus can be effectively prevented. The domain of the wavelength λ where λ1=350 and λ2=800 corresponds to a wavelength range including the whole visible region. The domain of the wavelength λ where λ1=380 and λ2=530 corresponds to a wavelength range of light transmitted through a blue (B) segment, the domain of the wavelength λ where λ1=450 and λ2=650 corresponds to a wavelength range of light transmitted through a green (G) segment, and the domain of the wavelength λ where λ1=530 and λ2=750 corresponds to a wavelength range of light transmitted through a red (R) segment, the segments composing a color filter mounted in a color image sensor. Since the requirements shown in Tables (II), (III), and (IV) are satisfied by the optical filter 1 a, the optical filter 1 a can be viewed as likely to be compatible with the characteristics of a color filter used in a camera.

As shown in the equation (1), differences each obtained by subtracting a spectral transmittance T_(θ2)(λ) at an incident angle of θ2° selected from 30° and 40° from a spectral transmittance T_(θ1)(λ) at an incident angle of θ1° (θ1<θ2) selected from 0° and 30° are integrated in the wavelength range of λ1 nm to λ2 nm to determine IE_(θ1/θ2) ^(λ1 to λ2). Therefore, by reference to IE_(θ1/θ2) ^(λ1 to λ2), a change in the shape of a spectral transmittance curve in the range of λ1 [nm]≤wavelength λ≤λ2 [nm] can be evaluated quantitatively in the case where the incident angle varies from θ1° to θ2°.

As shown in the equation (2), the absolute values of the differences each obtained by subtracting the spectral transmittance T_(θ2)(λ) at an incident angle of θ2° selected from 30° and 40° from the spectral transmittance T_(θ1)(λ) at an incident angle of θ1° (θ1<θ2) selected from 0° and 30° are integrated in the wavelength range of λ1 nm to λ2 nm to determine IAE_(θ1/θ2) ^(λ1 to λ2). It may sometimes be difficult to appropriately determine the characteristics of the optical filter only by the evaluation using IE_(θ1/θ2) ^(λ1 to λ2) because in the wavelength range of λ1 nm to λ2 nm, the integrated value obtained in a wavelength band in which differences obtained by subtracting T_(θ2)(λ) from T_(θ1)(λ) are negative can be offset by the integrated value obtained in a different wavelength band in which differences as described above are positive. By reference also to IAE_(θ1/θ2) ^(λ1 to λ2), the optical filter 1 a can be more appropriately evaluated.

As shown in the equation (3), the square values of the differences each obtained by subtracting the spectral transmittance T_(θ2)(λ) at an incident angle of θ2° selected from 300 and 40° from the spectral transmittance T_(θ1)(λ) at an incident angle of θ1° (θ1<θ2) selected from 0° and 30° are integrated in the wavelength range of λ1 nm to λ2 nm to determine ISE_(θ1/θ2) ^(λ1 to λ2). As described above, it may sometimes be difficult to appropriately determine the characteristics of the optical filter only by the evaluation using IE_(θ1/θ2) ^(λ1 to λ2). By reference also to ISE_(θ1/θ2) ^(λ1 to λ2), the optical filter 1 a can be more appropriately evaluated.

The light absorber included in the light-absorbing layer 10 is not particularly limited as long as the light absorber absorbs light in at least a portion of the near-infrared region, the optical filter 1 a satisfies the above requirements (i) to (vii), and the requirements shown in Tables (I) to (IV) are satisfied. The light absorber is, for example, formed by a phosphonic acid and copper ion. In this case, light in a wide wavelength band covering the near-infrared region and a part of the visible region adjacent to the near-infrared region can be absorbed by the light-absorbing layer 10. Therefore, the desired characteristics can be exhibited even when the optical filter 1 a does not include a reflecting film. When the optical filter 1 a includes a reflecting film, the optical filter 1 a can be designed so that the wavelength band of light reflected by the reflecting film will be sufficiently separated apart from the wavelength band of light to be transmitted. For example, the wavelength band of light reflected by the reflecting film can be set 100 nm or more away toward the long wavelength side from the wavelength band of a transition region in which the transmittance sharply decreases with increased wavelength. Thus, when the incident angle of light is large and the wavelength band of light reflected by the reflecting film shifts to the short wavelength side, the wavelength band of light reflected by the reflecting film overlaps with the wavelength band of light absorbed by the light-absorbing layer 10 and the transmittance characteristics of the optical filter 1 a in the transition region are unlikely to vary depending on the variation in incident angle of light. Additionally, light in a wide range included in the wavelength band of the ultraviolet region can be absorbed by the light-absorbing layer 10.

When the light-absorbing layer 10 includes the light absorber formed by a phosphonic acid and copper ion, the phosphonic acid includes, for example, a first phosphonic acid having an aryl group. In the first phosphonic acid, the aryl group is bonded to a phosphorus atom. Thus, the above requirements are easily satisfied by the optical filter 1 a.

The aryl group of the first phosphonic acid is, for example, a phenyl group, benzyl group, toluyl group, nitrophenyl group, hydroxyphenyl group, halogenated phenyl group in which at least one hydrogen atom of a phenyl group is substituted by a halogen atom, or halogenated benzyl group in which at least one hydrogen atom of a benzene ring of a benzyl group is substituted by a halogen atom.

When the light-absorbing layer 10 includes the light absorber formed by the phosphonic acid and copper ion, the phosphonic acid desirably further includes a second phosphonic acid having an alkyl group. In the second phosphonic acid, the alkyl group is bonded to a phosphorus atom.

The alkyl group of the second phosphonic acid is, for example, an alkyl group having 6 or less carbon atoms. This alkyl group may be linear or branched.

When the light-absorbing layer 10 includes the light absorber formed by the phosphonic acid and copper ion, the light-absorbing layer 10 desirably further includes a phosphoric acid ester allowing the light absorber to be dispersed and matrix resin.

The phosphoric acid ester included in the light-absorbing layer 10 is not limited to any particular one, as long as the phosphoric acid ester allows good dispersion of the light absorber. For example, the phosphoric acid ester includes at least one of a phosphoric acid diester represented by the following formula (c1) and a phosphoric acid monoester represented by the following formula (c2). In the formulae (c1) and (c2), R₂₁, R₂₂, and R₃ are each a monovalent functional group represented by —(CH₂CH₂O)_(n)R₄, wherein n is an integer of 1 to 25 and R₄ is an alkyl group having 6 to 25 carbon atoms. R₂₁, R₂₂, and R₃ may be the same or different functional groups.

The phosphoric acid ester is not particularly limited. The phosphoric acid ester can be, for example, PLYSURF A208N (polyoxyethylene alkyl (C12, C13) ether phosphoric acid ester), PLYSURF A208F (polyoxyethylene alkyl (C8) ether phosphoric acid ester), PLYSURF A208B (polyoxyethylene lauryl ether phosphoric acid ester), PLYSURF A219B (polyoxyethylene lauryl ether phosphoric acid ester), PLYSURF AL (polyoxyethylene styrenated phenylether phosphoric acid ester), PLYSURF A212C (polyoxyethylene tridecyl ether phosphoric acid ester), or PLYSURF A215C (polyoxyethylene tridecyl ether phosphoric acid ester). All of these are products manufactured by DKS Co., Ltd. The phosphoric acid ester can be NIKKOL DDP-2 (polyoxyethylene alkyl ether phosphoric acid ester), NIKKOL DDP-4 (polyoxyethylene alkyl ether phosphoric acid ester), or NIKKOL DDP-6 (polyoxyethylene alkyl ether phosphoric acid ester). All of these are products manufactured by Nikko Chemicals Co., Ltd.

The matrix resin included in the light-absorbing layer 10 is, for example, a heat-curable or ultraviolet-curable resin in which the light absorber is dispersible. Additionally, as the matrix resin can be used a resin that has a transmittance of, for example, 80% or more, preferably 85% or more, and more preferably 90% or more for light with a wavelength of 350 nm to 900 nm in the form of a 0.1-mm-thick resin layer. The matrix resin is not particularly limited as long as the above requirements (i) to (vii) and the requirements shown in Tables (I) to (IV) are satisfied by the optical filter 1 a. The content of the phosphonic acid in the light-absorbing layer 10 is, for example, 3 to 180 parts by mass with respect to 100 parts by mass of the matrix resin.

The matrix resin included in the light-absorbing layer 10 is not particularly limited as long as the above characteristics are satisfied. The matrix resin is, for example, a (poly)olefin resin, polyimide resin, polyvinyl butyral resin, polycarbonate resin, polyamide resin, polysulfone resin, polyethersulfone resin, polyamideimide resin, (modified) acrylic resin, epoxy resin, or silicone resin. The matrix resin may contain an aryl group such as a phenyl group and is desirably a silicone resin containing an aryl group such as a phenyl group. If the light-absorbing layer 10 is excessively hard (rigid), the likelihood of cure shrinkage-induced cracking during the production process of the optical filter 1 a increases with increasing thickness of the light-absorbing layer 10. When the matrix resin is a silicone resin containing an aryl group, the light-absorbing layer 10 is likely to have high crack resistance. Moreover, with the use of a silicone resin containing an aryl group, the light absorber formed by the above phosphonic acid and copper ion is less likely to be aggregated when included. Further, when the matrix resin of the light-absorbing layer 10 is a silicone resin containing an aryl group, it is desirable for the phosphoric acid ester included in the light-absorbing layer 10 to have a flexible, linear organic functional group, such as an oxyalkyl group, just as does the phosphoric acid ester represented by the formula (c1) or formula (c2). This is because interaction derived from the combination of the above phosphonic acid, a silicone resin containing an aryl group, and phosphoric acid ester having a linear organic functional group such as an oxyalkyl group makes aggregation of the light absorber less likely and can impart good rigidity and good flexibility to the light-absorbing layer. Specific examples of the silicone resin available as the matrix resin include KR-255, KR-300, KR-2621-1, KR-211, KR-311, KR-216, KR-212, and KR-251. All of these are silicone resins manufactured by Shin-Etsu Chemical Co., Ltd.

As shown in FIG. 1A, the optical filter 1 a further includes, for example, a transparent dielectric substrate 20. One principal surface of the transparent dielectric substrate 20 is covered with the light-absorbing layer 10. The characteristics of the transparent dielectric substrate 20 are not particularly limited as long as the above requirements (i) to (vii) and the requirements shown in Table (II) are satisfied by the optical filter 1 a. The transparent dielectric substrate 20 is a dielectric substrate having a high average transmittance (for example, 80% or more, preferably 85% or more, and more preferably 90% or more) in the wavelength range of, for example, 450 nm to 600 nm.

The transparent dielectric substrate 20 is, for example, made of glass or resin. When the transparent dielectric substrate 20 is made of glass, the glass is, for example, borosilicate glass such as D 263 T eco, soda-lime glass (blue plate glass), white sheet glass such as B 270, alkali-free glass, or infrared-absorbing glass such as copper-containing phosphate glass or copper-containing fluorophosphate glass. When the transparent dielectric substrate 20 is made of infrared-absorbing glass such as copper-containing phosphate glass or copper-containing fluorophosphate glass, the desired infrared absorption performance can be imparted to the optical filter 1 a by a combination of the infrared absorption performance of the transparent dielectric substrate 20 and the infrared absorption performance of the light-absorbing layer 10. Examples of such an infrared-absorbing glass include BG-60, BG-61, BG-62, BG-63, and BG-67 manufactured by SCHOTT AG, 500EXL manufactured by Nippon Electric Glass Co., Ltd., and CM5000, CM500, C5000, and C500S manufactured by HOYA CORPORATION. Moreover, the transparent dielectric substrate 20 may have ultraviolet absorption characteristics.

The transparent dielectric substrate 20 may be a transparent crystalline substrate, such as magnesium oxide, sapphire, or quartz. For example, sapphire is very hard and is thus scratch resistant. Therefore, as a scratch-resistant protective material (which may be called a protective filter or cover glass), a sheet-shaped sapphire is sometimes disposed ahead of a camera module or lens included in mobile devices such as smartphones and mobile phones. Formation of the light-absorbing layer 10 on such a sheet-shaped sapphire makes it possible to protect camera modules and lenses and cut off light with a wavelength of 650 nm to 1100 nm. This eliminates the need to dispose an optical filter that exhibits performance of shielding against infrared light with a wavelength of 650 nm to 1100 nm around an imaging device such as a charge-coupled device (CCD) sensor or complementary metal oxide semiconductor (CMOS) sensor or inside a camera module. Therefore, the formation of the light-absorbing layer 10 on a sheet-shaped sapphire can contribute to achievement of lower-profile camera modules and lower-profile imaging apparatuses.

When the transparent dielectric substrate 20 is made of resin, the resin is, for example, a (poly)olefin resin, polyimide resin, polyvinyl butyral resin, polycarbonate resin, polyamide resin, polysulfone resin, polyethersulfone resin, polyamideimide resin, (modified) acrylic resin, epoxy resin, or silicone resin.

The optical filter 1 a can be produced, for example, by applying a coating liquid for forming the light-absorbing layer 10 to one principal surface of the transparent dielectric substrate 20 to form a film and drying the film. The method for preparing the coating liquid and the method for producing the optical filter 1 a will be described with an example in which the light-absorbing layer 10 includes the light absorber formed by the phosphonic acid and copper ion.

First, an exemplary method for preparing the coating liquid will now be described. A copper salt such as copper acetate monohydrate is added to a given solvent such as tetrahydrofuran (THF), and the mixture is stirred to give a copper salt solution. To this copper salt solution is then added a phosphoric acid ester compound such as a phosphoric acid diester represented by the formula (c1) or a phosphoric acid monoester represented by the formula (c2), and the mixture is stirred to prepare a solution A. The first phosphonic acid is added to a given solvent such as THF, and the mixture is stirred to prepare a solution B. Next, the solution B is added to the solution A while the solution A is stirred, and the mixture is further stirred for a given period of time. To the resultant solution is then added a given solvent such as toluene, and the mixture is stirred to obtain a solution C. Subsequently, the solution C is subjected to solvent removal under heating for a given period of time to obtain a solution D. This process removes the solvent such as THF and the component such as acetic acid (boiling point: about 118° C.) generated by disassociation of the copper salt and yields a light absorber formed by the first phosphonic acid and copper ion. The temperature at which the solution C is heated is chosen based on the boiling point of the to-be-removed component disassociated from the copper salt. During the solvent removal, the solvent such as toluene (boiling point: about 110° C.) used to obtain the solution C is also evaporated. A certain amount of this solvent desirably remains in the coating liquid. This is preferably taken into account in determining the amount of the solvent to be added and the time period of the solvent removal. To obtain the solution C, o-xylene (boiling point: about 144° C.) may be used instead of toluene. In this case, the amount of o-xylene to be added can be reduced to about one-fourth of the amount of toluene to be added, because the boiling point of o-xylene is higher than the boiling point of toluene. A matrix resin such as a silicone resin is added to the solution D and the mixture is stirred. The coating liquid can thus be prepared.

The coating liquid is applied to one principal surface of the transparent dielectric substrate 20 to form a film. For example, the coating liquid is applied to one principal surface of the transparent dielectric substrate 20 by die coating or spin coating or with a dispenser to form a film. Next, this film is cured by a given heat treatment. For example, the film is exposed to an environment at a temperature of 50° C. to 200° C. for a given period of time.

In the optical filter 1 a, the light-absorbing layer 10 may be formed as a single layer or may be formed as a plurality of layers. When the light-absorbing layer 10 is formed as a plurality of layers, the light-absorbing layer 10 includes, for example, a first layer including the light absorber formed by the first phosphonic acid and copper ion and a second layer including the light absorber formed by the second phosphonic acid and copper ion. In this case, a coating liquid for forming the first layer can be prepared in the above manner. The second layer is formed using a coating liquid prepared separately from the coating liquid for forming the first layer. The coating liquid for forming the second layer can be prepared, for example, in the following manner.

A copper salt such as copper acetate monohydrate is added to a given solvent such as tetrahydrofuran (THF), and the mixture is stirred to give a copper salt solution. To this copper salt solution is then added a phosphoric acid ester compound such as a phosphoric acid diester represented by the formula (c1) or a phosphoric acid monoester represented by the formula (c2), and the mixture is stirred to prepare a solution E. The second phosphonic acid is added to a given solvent such as THF, and the mixture is stirred to prepare a solution F. Next, the solution F is added to the solution E while the solution E is stirred, and the mixture is further stirred for a given period of time. To the resultant solution is then added a given solvent such as toluene, and the mixture is stirred. The solvent is evaporated to obtain a solution G. Subsequently, a matrix resin such as a silicone resin is added to the solution G, and the mixture is stirred. The coating liquid for forming the second layer can thus be obtained.

The first and second layers can be formed by applying the coating liquid for forming the first layer and that for forming the second layer to form films, which are cured by a given heat treatment. For example, the films are exposed to an environment at a temperature of 50° C. to 200° C. for a given period of time. The order of forming the first and second layers is not particularly limited. The first and second layers may be formed in different time periods, or may be formed in the same time period. A protective layer may be formed between the first and second layers. The protective layer is formed of, for example, a SiO₂-deposited film.

<Modifications>

The optical filter 1 a can be modified in various respects. For example, the optical filter 1 a may be modified to optical filters 1 b to 1 f shown in FIG. 1B to FIG. 1F. The optical filters 1 b to if are configured in the same manner as the optical filter 1 a, unless otherwise described. The components of the optical filters 1 b to if that are the same as or correspond to those of the optical filter 1 a are denoted by the same reference characters, and detailed descriptions of such components are omitted. The description given for the optical filter 1 a can apply to the optical filters 1 b to 1 f, unless there is technical inconsistency.

As shown in FIG. 1B, the optical filter 1 b has the light-absorbing layers 10 formed on both principal surfaces of the transparent dielectric substrate 20. Therefore, the above requirements (i) to (vii) and the requirements shown in Table (II) are satisfied by the two light-absorbing layers 10 rather than one light-absorbing layer 10. The light-absorbing layers 10 on both principal surfaces of the transparent dielectric substrate 20 may have the same or different thicknesses. That is, the formation of the light-absorbing layers 10 on both principal surfaces of the transparent dielectric substrate 20 is done so that the two light-absorbing layers 10 account for equal or unequal proportions of the light-absorbing layer thickness required for the optical filter 1 b to have desired optical characteristics. Thus, each of the light-absorbing layers 10 formed on both principal surfaces of the transparent dielectric substrate 20 of the optical filter 1 b has a smaller thickness than the thickness of the light-absorbing layer 10 of the optical filter 1 a. The formation of the light-absorbing layers 10 on both principal surfaces of the transparent dielectric substrate 20 can reduce warping of the optical filter 1 b even when the transparent dielectric substrate 20 is thin. Each of the two light-absorbing layers 10 may be formed as a plurality of layers.

As shown in FIG. 1C, the optical filter 1 c has the light-absorbing layers 10 formed on both principal surfaces of the transparent dielectric substrate 20. The optical filter 1 c additionally includes an anti-reflection film 30. The anti-reflection film 30 is a film formed as an interface between the optical filter 1 c and air and reducing reflection of visible light. The anti-reflection film 30 is, for example, a film formed of a dielectric made of, for example, a resin, an oxide, or a fluoride. The anti-reflection film 30 may be a multilayer film formed by laminating two or more types of dielectrics having different refractive indices. The anti-reflection film 30 may be, particularly, a dielectric multilayer film made of a low-refractive-index material such as SiO₂ and a high-refractive-index material such as TiO₂ or Ta₂O₅. In this case, Fresnel reflection at the interface between the optical filter 1 and air is reduced and the amount of visible light transmitted through the optical filter 1 can be increased. The anti-reflection film 30 may be formed on both sides of the optical filter 1 c, or may be formed on one side thereof.

As shown in FIG. 1D, the optical filter 1 d has the light-absorbing layers 10 formed on both principal surfaces of the transparent dielectric substrate 20. Additionally, the optical filter 1 d further includes a reflecting film 40. The reflecting film 40 reflects infrared light and/or ultraviolet light. The reflecting film 40 is, for example, a film formed by vapor deposition of a metal such as aluminum or a dielectric multilayer film in which a layer formed of a high-refractive-index material and a layer formed of a low-refractive-index material are alternately laminated. A material, such as TiO₂, ZrO₂, Ta₂O₅, Nb₂O₅, ZnO, or In₂O₃, having a refractive index of 1.7 to 2.5 is used as the high-refractive-index material. A material, such as SiO₂, Al₂O₃, or MgF₂, having a refractive index of 1.2 to 1.6 is used as the low-refractive-index material. Examples of the method for forming the dielectric multilayer film include chemical vapor deposition (CVD), sputtering, and vacuum deposition. Such reflecting films may be formed to be both principal surfaces of the optical filter (not shown). The reflecting films formed on both principal surfaces of the optical filter balance the stress on the front side and that on the back side, and that offers an advantage of decreasing the likelihood of warping of the optical filter.

As shown in FIG. 1E, the optical filter 1 c consists only of the light-absorbing layer 10. The optical filter 1 c can be produced, for example, by applying the coating liquid onto a given substrate such as a glass substrate, resin substrate, or metal substrate (such as a steel substrate or stainless steel substrate) to form a film, curing the film, and then separating the film from the substrate. The optical filter 1 c may be produced by casting. Not including the transparent dielectric substrate 20, the optical filter 1 c is thin. The optical filter 1 c can thus contribute to achievement of lower-profile imaging apparatuses.

As shown in FIG. 1F, the optical filter if includes the light-absorbing layer 10 and a pair of the anti-reflection films 30 disposed on both sides of the light-absorbing layer 10. In this case, the optical filter if can contribute to achievement of lower-profile imaging apparatuses, and can increase the amount of visible light transmitted therethrough more than the optical filter 1 c can.

The optical filters 1 a to if may be modified to include an infrared-absorbing layer (not shown) in addition to the light-absorbing layer 10, if necessary. The infrared-absorbing layer includes, for example, an organic infrared absorber, such as a cyanine-based, phthalocyanine-based, squarylium-based, diimmonium-based, or azo-based infrared absorber or an infrared absorber composed of a metal complex. The infrared-absorbing layer includes, for example, one infrared absorber or two or more infrared absorbers selected from these infrared absorbers. The organic infrared absorber can absorb light in a relatively narrow wavelength range (absorption band) and is suitable for absorbing light with a given wavelength range.

The optical filters 1 a to if may be modified to include an ultraviolet-absorbing layer (not shown) in addition to the light-absorbing layer 10, if necessary. The ultraviolet-absorbing layer includes, for example, an ultraviolet absorber, such as a benzophenone-based, triazine-based, indole-based, merocyanine-based, or oxazole-based ultraviolet absorber. The ultraviolet-absorbing layer, for example, includes one ultraviolet absorber or two or more ultraviolet absorbers selected from these ultraviolet absorbers. The ultraviolet absorber can include ultraviolet absorbers absorbing ultraviolet light around a wavelength of, for example, 300 nm to 340° nm, emitting light (fluorescence) with a wavelength longer than the absorbed wavelength, and functioning as a fluorescent agent or fluorescent brightener. The ultraviolet-absorbing layer can reduce incidence of ultraviolet light which deteriorates the materials, such as resin, used in the optical filter.

The above infrared absorber and/or ultraviolet absorber may be contained beforehand in the transparent dielectric substrate 20 made of resin to form a substrate having characteristics of absorbing infrared light and/or ultraviolet light. In this case, it is necessary for the resin to allow the infrared absorber and/or ultraviolet absorber to be appropriately dissolved or dispersed therein and be transparent. Examples of such a resin include a (poly)olefin resin, polyimide resin, polyvinyl butyral resin, polycarbonate resin, polyamide resin, polysulfone resin, polyethersulfone resin, polyamideimide resin, (modified) acrylic resin, epoxy resin, and silicone resin.

As shown in FIG. 2 , the optical filter 1 a is used to produce, for example, an imaging apparatus 100 (camera module). The imaging apparatus 100 includes a lens system 2, an imaging device 4, a color filter 3, and the optical filter 1 a. The imaging device 4 receives light having been transmitted through the lens system 2. The color filter 3 is disposed ahead of the imaging device 4 and is a filter of three colors, R (red), G (green), and B (blue). The optical filter 1 a is disposed ahead of the color filter 3. The light-absorbing layer 10 is particularly arranged to be in contact with a side of the transparent dielectric substrate 20, the side being closer to the lens system 2. As described previously, the protecting effect on the lens system 2 or imaging device 4 increases when a hard material such as sapphire is used as the transparent dielectric substrate 20. For example, in the color filter 3, the three colors, R (red), G (green), and B (blue), are arranged in a matrix, and each of the R (red), G (green), and B (blue) colors is disposed immediately above a pixel of the imaging device 4. The imaging device 4 receives light coming from an object and having been transmitted through the lens system 2, optical filter 1 a, and color filter 3. The imaging apparatus 100 generates an image based on information on electric charge produced by the light received by the imaging device 4. The color filter 3 and imaging device 4 may be combined to configure a color image sensor.

The above requirements (i) to (vii) and the requirements shown in Table (II) are satisfied by the optical filter 1 a. The imaging apparatus 100 including the optical filter 1 a can therefore generate images uneven coloring of which is prevented.

EXAMPLES

The present invention will be described in more detail by examples. The present invention is not limited to the examples given below.

<Measurement of Transmittance Spectra>

Transmittance spectra shown upon incidence of light with wavelengths of 300 nm to 1200 nm on optical filters according to Examples and Comparative Examples, intermediate products thereof, and laminates according to Reference Examples were measured using an ultraviolet-visible spectrophotometer (manufactured by JASCO Corporation, product name: V-670). The incident angle of light incident on the optical filters of Examples and Comparative Examples, some of the intermediate products thereof, and some of the laminates according to Reference Examples was set to 0°, 30°, and 40° to measure the transmittance spectra thereof. The incident angle of light incident on the other intermediate products and the other laminates according to Reference Examples was set to 0° to measure the transmittance spectra thereof.

Example 1

A coating liquid IRA1 was prepared in the following manner. 1.1 g of copper acetate monohydrate and 60 g of tetrahydrofuran (THF) were mixed, followed by stirring for 3 hours. To the obtained solution was added 2.3 g of a phosphoric acid ester (manufactured by DKS Co., Ltd., product name: PLYSURF A208F), followed by stirring for 30 minutes to obtain a solution A. 10 g of THF was added to 0.6 g of phenylphosphonic acid (manufactured by Tokyo Chemical Industry Co., Ltd.), followed by stirring for 30 minutes to obtain a solution B. The solution B was added to the solution A while the solution A was stirred, and the mixture was stirred at room temperature for 1 minute. To the resultant solution was added 45 g of toluene, followed by stirring at room temperature for 1 minute to obtain a solution C. The solution C was placed in a flask and subjected to solvent removal for 25 minutes using a rotary evaporator (manufactured by Tokyo Rikakikai Co., Ltd., product code: N-1110SF) under heating by means of an oil bath (manufactured by Tokyo Rikakikai Co., Ltd., product code: OSB-2100) controlled to 120° C. A solution D was thus obtained. The solution D was taken out of the flask, and to the solution D was added 4.4 g of a silicone resin (manufactured by Shin-Etsu Chemical Co., Ltd., product name: KR-300), followed by stirring at room temperature for 30 minutes to obtain a coating liquid IRA1.

A coating liquid IRA2 was prepared in the following manner. 2.25 g of copper acetate monohydrate and 120 g of tetrahydrofuran (THF) were mixed, followed by stirring for 3 hours. To the obtained solution was added 1.8 g of a phosphoric acid ester (manufactured by DKS Co., Ltd., product name: PLYSURF A208F), followed by stirring for 30 minutes to obtain a solution E. 20 g of THF was added to 1.35 g of butylphosphonic acid, followed by stirring for 30 minutes to obtain a solution F. The solution F was added to the solution E while the solution E was stirred, and the mixture was stirred at room temperature for 3 hours. To the resultant solution was added 40 g of toluene, and the solvent was evaporated in an 85° C. environment over 7.5 hours to obtain a solution G. To the solution G was added 8.8 g of a silicone resin (manufactured by Shin-Etsu Chemical Co., Ltd., product name: KR-300), followed by stirring for 3 hours to obtain a solution IRA2.

The coating liquid IRA1 was applied to one principal surface of a transparent glass substrate (manufactured by SCHOTT AG, product name: D 263 T eco) using a die coater. The resultant film was cured by heat treatment in an oven at 85° C. for 3 hours, at 125° C. for 3 hours, at 150° C. for 1 hour, and then at 170° C. for 3 hours to form an infrared-absorbing layer ira11. In the same manner, the coating liquid IRA1 was applied to the other principal surface of the transparent glass substrate. The resultant film was cured by heat treatment under the same conditions as above to form an infrared-absorbing layer ira12. An intermediate product a of an optical filter according to Example 1 was thus obtained. The total thickness of the infrared-absorbing layer ira11 and infrared-absorbing layer ira12 is 0.2 mm. A transmittance spectrum shown by the intermediate product a at an incident angle of 0° is shown in FIG. 3A. The intermediate product a has the following characteristics (α1) to (α6).

(α1): The average transmittance in the wavelength range of 700 to 1000 nm is 0.5% or less.

(α2): The average transmittance in the wavelength range of 1100 to 1200 nm is 29.5%.

(α3): The average transmittance in the wavelength range of 450 to 600 nm is 88.0%.

(α4): The transmittance at a wavelength of 40° nm is 63.7%.

(α5): The IR cut-off wavelength is 632 nm, the UV cut-off wavelength is 394 nm, and when the difference between the IR cut-off wavelength and UV cut-off wavelength is regarded as a full width at half maximum in a transmission region, the full width at half maximum in the transmission region is 238 nm.

(α6): The wavelength which lies in the wavelength range of 600 to 800 nm and at which the spectral transmittance is 20% is 661 nm.

A 500-nm-thick SiO₂-deposited film (protective layer p1) was formed on the infrared-absorbing layer ira11 of the intermediate product a using a vacuum deposition apparatus. In the same manner, a 500-nm-thick SiO₂-deposited film (protective layer p2) was formed on the infrared-absorbing layer ira12 of the intermediate product a. The coating liquid IRA2 was applied to the surface of the protective layer p1 with a die coater. The resultant film was cured by heat treatment in an oven at 85° C. for 3 hours, at 125° C. for 3 hours, at 150° C. for 1 hour, and then at 170° C. for 3 hours to form an infrared-absorbing layer ira21. The coating liquid IRA2 was applied also to the surface of the protective layer p2 with a die coater. The resultant film was cured under the same heating conditions to form an infrared-absorbing layer ira22. An intermediate product 8 was thus obtained. The total thickness of the infrared-absorbing layer ira21 and infrared-absorbing layer ira22 is 50 μm. A transmittance spectrum of the intermediate product ß is shown in FIG. 3B. The intermediate product β has the following characteristics (ß1) to (ß6).

(ß1): The average transmittance in the wavelength range of 700 to 1000 nm is 0.5% or less.

(ß2): The average transmittance in the wavelength of 1100 to 1200 nm is 4.5%.

(ß3): The average transmittance in the wavelength range of 450 to 600 nm is 86.9%.

(ß4): The transmittance at a wavelength of 40° nm is 62.1%.

(ß5): The IR cut-off wavelength is 631 nm, the UV cut-off wavelength is 394 nm, and the full width at half maximum of the transmission region is 237 nm.

(ß6): The wavelength which lies in the wavelength range of 600 to 800 nm and at which the spectral transmittance is 20% is 659 nm.

A 500-nm-thick SiO₂-deposited film (protective layer p3) was formed on the infrared-absorbing layer ira22 of the intermediate product 8 using a vacuum deposition apparatus.

A coating liquid UVA1 was prepared in the following manner. A benzophenone-based ultraviolet-absorbing substance having low light absorption in the visible region and soluble in methyl ethyl ketone (MEK) was used as an ultraviolet-absorbing substance. This ultraviolet-absorbing substance was dissolved in MEK serving as a solvent, to which polyvinyl butyral (PVB) in which the solids account for 60 weight % was added, followed by stirring for 2 hours to obtain a coating liquid UVA1. The coating liquid UVA1 was applied onto the protective layer p3 by spin coating, followed by curing by heating at 140° C. for 30 minutes to form an ultraviolet-absorbing layer uva1. The thickness of the ultraviolet-absorbing layer uva1 is 6 μm. Separately, a laminate according to Reference Example 1 was obtained by forming a 6-μm-thick ultraviolet-absorbing layer on a surface of a transparent glass substrate (manufactured by SCHOTT AG, product name: D 263 T eco) using the coating liquid UVA1 by spin coating. A transmittance spectrum of the laminate according to Reference Example 1 is shown in FIG. 3C. The laminate according to Reference Example 1 has the following characteristics (r1) to (r3).

(r1): The transmittance in the wavelength range of 350 to 390 nm is 0.5% or less.

(r2): The transmittance at a wavelength of 40° nm is 12.9%, the transmittance at a wavelength of 410 nm is 51.8%, the transmittance at a wavelength of 420 nm is 77.1%, and the transmittance at a wavelength of 450 nm is 89.8%.

(r3): The average transmittance in the wavelength range of 450 to 750 nm is 91.0%.

An anti-reflection film ar1 was formed on the infrared-absorbing layer ira21 using a vacuum deposition apparatus. An anti-reflection film ar2 was formed on the ultraviolet-absorbing layer uva1 using a vacuum deposition apparatus. The specifications of the anti-reflection film ar1 and anti-reflection film ar2 are the same. Each of the anti-reflection film ar1 and anti-reflection film ar2 is a film composed of SiO₂ and TiO₂ that are alternately laminated, includes 7 layers, and has a total thickness of about 0.4 μm. An optical filter according to Example 1 was thus obtained. An anti-reflection film was formed on one side of a transparent glass substrate (manufactured by SCHOTT AG, product name: D 263 T eco) under the same conditions as for the formation of the anti-reflection film ar1 to obtain a laminate according to Reference Example 2. Transmittance spectra of the laminate according to Reference Example 2 are shown in FIG. 3D. The laminate according to Reference Example 2 has the following characteristics (s1) to (s4).

(s1): When the incident angle of light is 0°, the transmittance at a wavelength of 350 nm is 73.4%, the transmittance at a wavelength of 380 nm is 88.9%, the transmittance at a wavelength of 40° nm is 95.3%, the average transmittance in the wavelength range of 40° to 700 nm is 95.3%, and the transmittance at a wavelength of 715 nm is 95.7%.

(s2): When the incident angle of light is 30°, the transmittance at a wavelength of 350 nm is 78.5%, the transmittance at a wavelength of 380 nm is 92.0%, the transmittance at a wavelength of 40° nm is 94.5%, the average transmittance in the wavelength range of 40° to 700 nm is 94.3%, and the transmittance at a wavelength of 715 nm is 94.6%.

(s3): When the incident angle of light is 40°, the transmittance at a wavelength of 350 nm is 82.3%, the transmittance at a wavelength of 380 nm is 93.3%, the transmittance at a wavelength of 40° nm is 94.3%, the average transmittance in the wavelength range of 40° to 700 nm is 94.0%, and the transmittance at a wavelength of 715 nm is 94.1%.

(s4): In the wavelength range of 40° to 700 nm, there is no wavelength band in which a ripple, i.e., a local decrease in transmittance, occurs, regardless of the incident angle of light.

Transmittance spectra of the optical filter according to Example 1 are shown in FIG. 3E and Table 9. The optical filter according to Example 1 has the characteristics shown in Table 10. A relationship between wavelengths and differences between spectral transmittances of the optical filter according to Example 1 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 4A. A relationship between wavelengths and the absolute values of the differences between spectral transmittances of the optical filter according to Example 1 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 4B. A relationship between wavelengths and the square values of the differences between spectral transmittances of the optical filter according to Example 1 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 4C. IE_(θ1/θ2) ^(λ1 to λ2), IAE_(θ1/θ2) ^(λ1 to λ2), and ISE_(θ1/θ2) ^(λ1 to λ2) were determined by the above equations (1) to (3) from the transmittance spectra of the optical filter according to Example 1 at incident angles of 0°, 30°, and 40°. IE_(θ1/θ2) ^(λ1 to λ2), IAE_(θ1/θ2) ^(λ1 to λ2), and ISE_(θ1/θ2) ^(λ1 to λ2) to were determined in the domain of the wavelength λ where λ1=350 and λ2=800, the domain of the wavelength λ where λ1=380 and λ2=530, the domain of the wavelength λ where λ1=450 and λ2=650, and the domain of the wavelength λ where λ1=530 and λ2=750. The results are shown in Tables 11 to 14.

Example 2

Coating liquids IRA1 and IRA2 were prepared in the same manner as in Example 1. The coating liquid IRA1 was applied to one principal surface of a transparent glass substrate (manufactured by SCHOTT AG, product name: D 263 T eco) using a die coater. The resultant film was cured by heat treatment in an oven at 85° C. for 3 hours, at 125° C. for 3 hours, at 150° C. for 1 hour, and then at 170° C. for 3 hours to form an infrared-absorbing layer ira11. In the same manner, the coating liquid IRA1 was applied to the other principal surface of the transparent glass substrate. The resultant film was cured by heat treatment under the same conditions as above to form an infrared-absorbing layer ira12. The total thickness of the infrared-absorbing layer ira11 and infrared-absorbing layer ira12 is 0.2 mm.

A 500-nm-thick SiO₂-deposited film (protective layer p1) was formed on the infrared-absorbing layer ira11 using a vacuum deposition apparatus. In the same manner, a 500-nm-thick SiO₂-deposited film (protective layer p2) was formed on the infrared-absorbing layer ira12. The coating liquid IRA2 was applied to the surface of the protective layer p1 with a die coater. The resultant film was cured by heat treatment in an oven at 85° C. for 3 hours, at 125° C. for 3 hours, at 150° C. for 1 hour, and then at 170° C. for 3 hours to form an infrared-absorbing layer ira21. The coating liquid IRA2 was applied also to the surface of the protective layer p2 with a die coater. The resultant film was cured under the same heating conditions to form an infrared-absorbing layer ira22. The total thickness of the infrared-absorbing layer ira21 and infrared-absorbing layer ira22 is 50 μm.

A 500-nm-thick SiO₂-deposited film (protective layer p3) was formed on the infrared-absorbing layer ira22 using a vacuum deposition apparatus. A coating liquid UVIRA1 containing an infrared-absorbing dye and ultraviolet-absorbing dye was prepared in the following manner. The infrared-absorbing dye is a combination of a cyanine-based organic dye and squarylium-based organic dye, has an absorption peak in the wavelength range of 680 to 780 nm, and is less likely to absorb light in the visible region. The ultraviolet-absorbing dye is a dye composed of a benzophenone-based ultraviolet-absorbing substance which is less likely to absorb light in the visible region. The infrared-absorbing dye and ultraviolet-absorbing dye are soluble in MEK. The infrared-absorbing dye and ultraviolet-absorbing dye were added to MEK serving as a solvent, and PVB serving as a matrix was also added thereto, followed by stirring for 2 hours to obtain a coating liquid UVIRA1. The content of the infrared-absorbing dye and the content of the ultraviolet-absorbing dye in the coating liquid UVIRA1 were determined so that a laminate according to Reference Example 3 would show a transmittance spectrum as shown in FIG. 5A The laminate according to Reference Example 3 was produced by applying the coating liquid UVIRA1 onto a transparent glass substrate (manufactured by SCHOTT AG, product name: D 263 T eco) by spin coating, and curing the resultant film by heating at 140° C. for 30 minutes. In the coating liquid UVIRA1, the mass ratio (mass of infrared-absorbing dye:mass of solids of PVB) between the infrared-absorbing dye and the solids of PVB is about 1:199. The mass ratio (mass of ultraviolet-absorbing dye:mass of solids of PVB) between the ultraviolet-absorbing dye and the solids of PVB is about 40:60. The laminate according to Reference Example 3 has the following characteristics (t1) to (t5).

(t1): The transmittance at a wavelength of 700 nm is 8.7%, the transmittance at a wavelength of 715 nm is 13.6%, and the average transmittance in the wavelength range of 700 to 800 nm is 66.2%.

(t2): The transmittance at a wavelength of 1100 nm is 92.1%.

(t3): The transmittance at a wavelength of 40° nm is 11.8%, the transmittance at a wavelength of 450 nm is 85.3%, and the average transmittance in the wavelength range of 500 to 600 nm is 89.1%.

(t4): The IR cut-off wavelength in the wavelength range of 600 nm to 700 nm is 669 nm, the IR cut-off wavelength in the wavelength range of 700 nm to 800 nm is 729 nm, and the difference therebetween is 60 nm. The wavelength (wavelength of maximum absorption) at which the transmittance is the lowest in the wavelength range of 600 nm to 800 nm is 705 nm.

(t5): The UV cut-off wavelength in the wavelength range of 350 nm to 450 nm is 411 nm.

The coating liquid UVIRA1 was applied onto the protective layer p3 by spin coating, and the resultant film was cured by heating at 140° C. for 30 minutes to form an infrared- and ultraviolet-absorbing layer uvira1. The thickness of the infrared- and ultraviolet-absorbing layer uvira1 is 7 μm.

An anti-reflection film ar1 was formed on the infrared-absorbing layer ira21 using a vacuum deposition apparatus. An anti-reflection film ar2 was formed on the infrared- and ultraviolet-absorbing layer uvira1 using a vacuum deposition apparatus. The specifications of the anti-reflection film ar1 and anti-reflection film ar2 are the same. Each of the anti-reflection film ar1 and anti-reflection film ar2 is a film composed of SiO₂ and TiO₂ that are alternately laminated, includes 7 layers, and has a total thickness of about 0.4 μm. An optical filter according to Example 2 was thus obtained.

Transmittance spectra of the optical filter according to Example 2 are shown in FIG. 5B and Table 15. The optical filter according to Example 2 has the characteristics shown in Table 16. A relationship between wavelengths and differences between spectral transmittances of the optical filter according to Example 2 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 6A. A relationship between wavelengths and the absolute values of the differences between spectral transmittances of the optical filter according to Example 2 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 6B. A relationship between wavelengths and the square values of the differences between spectral transmittances of the optical filter according to Example 2 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 6C. IE_(θ1/θ2) ^(λ1 to λ2), IAE_(θ1/θ2) ^(λ1 to λ2), and ISE_(θ1/θ2) ^(λ1 to λ2) were determined by the above equations (1) to (3) from the transmittance spectra of the optical filter according to Example 1 at incident angles of 0°, 30°, and 40°. IE_(θ1/θ2) ^(λ1 to λ2), IAE_(θ1/θ2) ^(λ1 to λ2), and ISE_(θ1/θ2) ^(λ1 to λ2) were determined in the domain of the wavelength λ where λ1=350 and λ2=800, the domain of the wavelength λ where λ1=380 and λ2=530, the domain of the wavelength λ where λ1=450 and λ2=650, and the domain of the wavelength λ where λ1=530 and λ2=750. The results are shown in Tables 17 to 20.

Example 3

Coating liquids IRA1 and IRA2 were prepared in the same manner as in Example 1. The coating liquid IRA1 was applied to one principal surface of a transparent glass substrate (manufactured by SCHOTT AG, product name: D 263 T eco) using a die coater. The resultant film was cured by heat treatment in an oven at 85° C. for 3 hours, at 125° C. for 3 hours, at 150° C. for 1 hour, and then at 170° C. for 3 hours to form an infrared-absorbing layer ira11. In the same manner, the coating liquid IRA1 was applied to the other principal surface of the transparent glass substrate. The resultant film was cured by heat treatment under the same conditions as above to form an infrared-absorbing layer ira12. An intermediate product γ of an optical filter according to Example 3 was thus obtained. The total thickness of the infrared-absorbing layer ira11 and infrared-absorbing layer ira12 is 0.2 mm. A transmittance spectrum shown by the intermediate product γ at an incident angle of 0° is shown in FIG. 7A. The intermediate product γ has the following characteristics (γ1) to (γ6).

(γ1): The average transmittance in the wavelength range of 700 to 1000 nm is 0.5% or less.

(γ2): The average transmittance in the wavelength range of 1100 to 1200 nm is 25.9%.

(γ3): The average transmittance in the wavelength range of 450 to 600 nm is 87.5%.

(γ4): The transmittance at a wavelength of 40° nm is 60.9%.

(γ5): The IR cut-off wavelength is 629 nm, the UV cut-off wavelength is 395 nm, and the full width at half maximum in the transmission region is 234 nm.

(γ6): The wavelength which lies in the wavelength range of 600 to 800 nm and at which the spectral transmittance is 20% is 657 nm.

A 500-nm-thick SiO₂-deposited film (protective layer p2) was formed on the infrared-absorbing layer ira12 of the intermediate product γ. A coating liquid UVA1 as used in Example 1 was applied onto the protective layer p2 by spin coating and the resultant film was cured by heating at 140° C. for 30 minutes to form an ultraviolet-absorbing layer uva1. The thickness of the ultraviolet-absorbing layer uva1 is 6 μm.

An anti-reflection film ar1 was formed on the infrared-absorbing layer ira11 using a vacuum deposition apparatus. An anti-reflection film ar2 was formed on the ultraviolet-absorbing layer uva1 using a vacuum deposition apparatus. The specifications of the anti-reflection film ar1 and anti-reflection film ar2 are the same. Each of the anti-reflection film ar1 and anti-reflection film ar2 is a film composed of SiO₂ and TiO₂ that are alternately laminated, includes 7 layers, and has a total thickness of about 0.4 μm. An optical filter according to Example 3 was thus obtained.

Transmittance spectra of the optical filter according to Example 3 are shown in FIG. 7B and Table 21. The optical filter according to Example 3 has the characteristics shown in Table 22. A relationship between wavelengths and differences between spectral transmittances of the optical filter according to Example 3 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 8A. A relationship between wavelengths and the absolute values of the differences between spectral transmittances of the optical filter according to Example 3 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 8B. A relationship between wavelengths and the square values of the differences between spectral transmittances of the optical filter according to Example 3 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 8C. IE_(θ1/θ2) ^(λ1 to λ2), IAE_(θ1/θ2) ^(λ1 to λ2), and ISE_(θ1/θ2) ^(λ1 to λ2) were determined in the domain of the wavelength λ where λ1=350 and λ2=800, the domain of the wavelength λ where λ1=380 and λ2=530, the domain of the wavelength λ where λ1=450 and λ2=650, and the domain of the wavelength λ where λ1=530 and λ2=750. The results are shown in Tables 23 to 26.

Example 4

A coating liquid IRA1 was prepared in the same manner as in Example 1. The coating liquid IRA1 was applied to one principal surface of a transparent glass substrate (manufactured by SCHOTT AG, product name: D 263 T eco) using a die coater. The resultant film was cured by heat treatment in an oven at 85° C. for 3 hours, at 125° C. for 3 hours, at 150° C. for 1 hour, and then at 170° C. for 3 hours to form an infrared-absorbing layer ira11. In the same manner, the coating liquid IRA1 was applied to the other principal surface of the transparent glass substrate. The resultant film was cured by heat treatment under the same conditions as above to form an infrared-absorbing layer ira12. The total thickness of the infrared-absorbing layer ira11 and infrared-absorbing layer ira12 is 0.2 mm.

Next, an infrared-reflecting film irr1 was formed on the infrared-absorbing layer ira11 using a vacuum deposition apparatus. The infrared-reflecting film irr1 is composed of SiO₂ and TiO₂ that are alternately laminated in 16 layers. An infrared-reflecting film was formed on one principal surface of a transparent glass substrate (manufactured by SCHOTT AG, product name: D 263 T eco) under the same conditions as for the formation of the infrared-reflecting film irr1 to produce a laminate according to Reference Example 4. Transmittance spectra of the laminate according to Reference Example 4 are shown in FIG. 9A. The laminate according to Reference Example 4 has the following characteristics (u1) to (u3).

(u1): When the incident angle of light is 0°, the transmittance at a wavelength of 380 nm is 1.8%, the transmittance at a wavelength of 40° nm is 7.3%, the average transmittance in the wavelength range of 450 to 700 nm is 94.8%, the lowest transmittance in the wavelength range of 450 to 700 nm is 93.4%, the average transmittance in the wavelength range of 700 to 800 nm is 94.0%, the transmittance at a wavelength of 1100 nm is 4.1%, the IR cut-off wavelength is 902 nm, and the UV cut-off wavelength is 410 nm.

(u2): When the incident angle of light is 30°, the transmittance at a wavelength of 380 nm is 1.8%, the transmittance at a wavelength of 40° nm is 67.8%, the average transmittance in the wavelength range of 450 to 700 nm is 95.0%, the lowest transmittance in the wavelength range of 450 to 700 nm is 93.8%, the average transmittance in the wavelength range of 700 to 800 nm is 92.1%, the transmittance at a wavelength of 1100 nm is 5.3%, the IR cut-off wavelength is 863 nm, and the UV cut-off wavelength is 398 nm.

(u3): When the incident angle of light is 40°, the transmittance at a wavelength of 380 nm is 4.0%, the transmittance at a wavelength of 40° nm is 90.2%, the average transmittance in the wavelength range of 450 to 700 nm is 94.1%, the lowest transmittance in the wavelength range of 450 to 700 nm is 92.9%, the average transmittance in the wavelength range of 700 to 800 nm is 91.5%, the transmittance at a wavelength of 1100 nm is 8.3%, the IR cut-off wavelength is 837 nm, and the UV cut-off wavelength is 391 nm.

A 500-nm-thick SiO₂-deposited film (protective layer p2) was formed on the infrared-absorbing layer ira12. A coating liquid UVA1 as used in Example 1 was applied onto the protective layer p2 by spin coating and the resultant film was cured by heating at 140° C. for 30 minutes to form an ultraviolet-absorbing layer uva1. The thickness of the ultraviolet-absorbing layer uva1 is 6 μm. An anti-reflection film ar2 was formed on the ultraviolet-absorbing layer uva1 using a vacuum deposition apparatus. The anti-reflection film ar2 is a film composed of SiO₂ and TiO₂ that are alternately laminated, includes 7 layers, and has a total thickness of about 0.4 μm. An optical filter according to Example 4 was thus obtained.

Transmittance spectra of the optical filter according to Example 4 are shown in FIG. 9B and Table 27. The optical filter according to Example 4 has the characteristics shown in Table 28. A relationship between wavelengths and differences between spectral transmittances of the optical filter according to Example 4 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 10A. A relationship between wavelengths and the absolute values of the differences between spectral transmittances of the optical filter according to Example 4 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 10B. A relationship between wavelengths and the square values of the differences between spectral transmittances of the optical filter according to Example 4 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 10C. IE_(θ1/θ2) ^(λ1 to λ2), IAE_(θ1/θ2) ^(λ1 to λ2), and ISE_(θ1/θ2) ^(λ1 to λ2) were determined in the domain of the wavelength λ where λ1=350 and λ2=800, the domain of the wavelength λ where λ1=380 and λ2=530, the domain of the wavelength λ where λ1=450 and λ2=650, and the domain of the wavelength λ where λ1=530 and λ2=750. The results are shown in Tables 29 to 32.

Example 5

A coating liquid IRA1 was prepared in the same manner as in Example 1. The coating liquid IRA1 was applied to one principal surface of a transparent glass substrate (manufactured by SCHOTT AG, product name: D 263 T eco) using a die coater. The resultant film was cured by heat treatment in an oven at 85° C. for 3 hours, at 125° C. for 3 hours, at 150° C. for 1 hour, and then at 170° C. for 3 hours to form an infrared-absorbing layer ira11. In the same manner, the coating liquid IRA1 was applied to the other principal surface of the transparent glass substrate. The resultant film was cured by heat treatment under the same conditions as above to form an infrared-absorbing layer ira12. The total thickness of the infrared-absorbing layer ira11 and infrared-absorbing layer ira12 is 0.2 mm.

Next, an infrared-reflecting film irr1 was formed on the infrared-absorbing layer ira11 using a vacuum deposition apparatus in the same manner as in Example 4. The infrared-reflecting film irr1 is composed of SiO₂ and Ti₂ that are alternately laminated in 16 layers.

A 500-nm-thick SiO₂-deposited film (protective layer p2) was formed on the infrared-absorbing layer ira12. A coating liquid UVRA1 as used in Example 2 was applied onto the protective layer p2 under the same conditions as in Example 2 and the resultant film was cured by heating at 140° C. for 30 minutes to form an infrared- and ultraviolet-absorbing layer uvira1. The thickness of the infrared- and ultraviolet-absorbing layer uvira1 is 7 μm. An anti-reflection film ar2 was formed on the infrared- and ultraviolet-absorbing layer uvira1 using a vacuum deposition apparatus. The anti-reflection film ar2 is a film composed of SiO₂ and TiO₂ that are alternately laminated, includes 7 layers, and has a total thickness of about 0.4 μm. An optical filter according to Example 5 was thus obtained.

Transmittance spectra of the optical filter according to Example 5 are shown in FIG. 11 and Table 33. The optical filter according to Example 5 has the characteristics shown in Table 34. A relationship between wavelengths and differences between spectral transmittances of the optical filter according to Example 5 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 12A. A relationship between wavelengths and the absolute values of the differences between spectral transmittances of the optical filter according to Example 5 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 12B. A relationship between wavelengths and the square values of the differences between spectral transmittances of the optical filter according to Example 5 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 12C. IE_(θ1/θ2) ^(λ1 to λ2), IAE_(θ1/θ2) ^(λ1 to λ2), and ISE_(θ1/θ2) ^(λ1 to λ2) were determined in the domain of the wavelength λ where λ1=350 and λ2=800, the domain of the wavelength λ where λ1=380 and λ2=530, the domain of the wavelength λ where λ1=450 and λ=650, and the domain of the wavelength λ where λ1=530 and λ2=750. The results are shown in Tables 35 to 38.

Example 6

Coating liquids IRA1 and IRA2 were prepared in the same manner as in Example 1. The coating liquid IRA1 was applied to one principal surface of a transparent glass substrate (manufactured by SCHOTT AG, product name: D 263 T eco) using a die coater. The resultant film was cured by heat treatment in an oven at 85° C. for 3 hours, at 125° C. for 3 hours, at 150° C. for 1 hour, and then at 170° C. for 3 hours to form an infrared-absorbing layer ira11. In the same manner, the coating liquid IRA1 was applied to the other principal surface of the transparent glass substrate. The resultant film was cured by heat treatment under the same conditions as above to form an infrared-absorbing layer ira12. The total thickness of the infrared-absorbing layer ira11 and infrared-absorbing layer ira12 is 0.4 mm.

A 500-nm-thick SiO₂-deposited film (protective layer p1) was formed on the infrared-absorbing layer ira11 using a vacuum deposition apparatus. In the same manner, a 500-nm-thick SiO₂-deposited film (protective layer p2) was formed on the infrared-absorbing layer ira12. The coating liquid IRA2 was applied to the surface of the protective layer p1 with a die coater. The resultant film was cured by heat treatment in an oven at 85° C. for 3 hours, at 125° C. for 3 hours, at 150° C. for 1 hour, and then at 170° C. for 3 hours to form an infrared-absorbing layer ira21. The coating liquid IRA2 was applied also to the surface of the protective layer p2 with a die coater. The resultant film was cured under the same heating conditions to form an infrared-absorbing layer ira22. An intermediate product δ was thus obtained. A transmittance spectrum shown by the intermediate product δ at an incident angle of 0° is shown in FIG. 13A. The intermediate product δ has the following characteristics (δ1) to (δ8).

(δ1): The average transmittance in the wavelength range of 700 to 1100 nm is 0.5% or less.

(δ2): The average transmittance in the wavelength range of 700 to 1000 nm is 0.5% or less.

(δ3): The average transmittance in the wavelength range of 1100 to 1200 nm is 0.5% or less.

(δ4): The average transmittance in the wavelength range of 450 to 600 nm is 82.2%.

(δ5): The average transmittance in the wavelength range of 500 to 600 nm is 82.7%.

(δ6): The transmittance at a wavelength of 400 nm is 42.0% and the transmittance at a wavelength of 450 nm is 76.7%.

(δ7): The IR cut-off wavelength is 613 nm, the UV cut-off wavelength is 404 nm, and the full width at half maximum of the transmission region is 209 nm.

(δ8): The wavelength which lies in the wavelength range of 600 to 800 nm and at which the spectral transmittance is 20% is 637 nm.

An anti-reflection film ar1 was formed on the infrared-absorbing layer ira21 using a vacuum deposition apparatus. An anti-reflection film ar2 was formed on the infrared-absorbing layer ira22 using a vacuum deposition apparatus. The specifications of the anti-reflection film ar1 and anti-reflection film ar2 are the same. Each of the anti-reflection film ar1 and anti-reflection film ar2 is a film composed of SiO₂ and TiO₂ that are alternately laminated, includes 7 layers, and has a total thickness of about 0.4 μm. An optical filter according to Example 6 was thus obtained.

Transmittance spectra of the optical filter according to Example 6 are shown in FIG. 13B and Table 39. The optical filter according to Example 6 has the characteristics shown in Table 40. A relationship between wavelengths and differences between spectral transmittances of the optical filter according to Example 6 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 14A. A relationship between wavelengths and the absolute values of the differences between spectral transmittances of the optical filter according to Example 6 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 14B. A relationship between wavelengths and the square values of the differences between spectral transmittances of the optical filter according to Example 6 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 14C. IE_(θ1/θ2) ^(λ1 to λ2), IAE_(θ1/θ2) ^(λ1 to λ2), and ISE_(θ1/θ2) ^(λ1 to λ2) were determined in the domain of the wavelength λ where λ1=350 and λ2=800, the domain of the wavelength λ where λ1=380 and λ2=530, the domain of the wavelength λ where λ1=450 and λ2=650, and the domain of the wavelength λ where λ1=530 and λ2=750. The results are shown in Tables 41 to 44.

Comparative Example 1

An infrared-reflecting film irr2 was formed on one principal surface of a transparent glass substrate (manufactured by SCHOTT AG, product name: D 263 T eco) by alternately laminating SiO₂ and TiO₂ in 24 layers using a vacuum deposition apparatus. An intermediate product ε was thus obtained. Transmittance spectra of the intermediate product ε are shown in FIG. 15A. The intermediate product ε has the following characteristics (ε1) to (ε3).

(ε1): When the incident angle of light is 0°, the transmittance at a wavelength of 380 nm is 0.5% or less, the transmittance at a wavelength of 40° nm is 3.1%, the average transmittance in the wavelength range of 450 to 600 nm is 94.1%, the lowest transmittance in the wavelength range of 450 to 600 nm is 92.6%, the transmittance at a wavelength of 700 nm is 86.2%, the transmittance at a wavelength of 715 nm is 30.8%, the average transmittance in the wavelength range of 700 to 800 nm is 12.4%, the transmittance at a wavelength of 1100 nm is 0.5% or less, the IR cut-off wavelength is 710 nm, and the UV cut-off wavelength is 410 nm.

(ε2): When the incident angle of light is 30°, the transmittance at a wavelength of 380 nm is 1.7%, the transmittance at a wavelength of 40° nm is 77.7%, the average transmittance in the wavelength range of 450 to 600 nm is 94.1%, the lowest transmittance in the wavelength range of 450 to 600 nm is 93.0%, the transmittance at a wavelength of 700 nm is 8.2%, the transmittance at a wavelength of 715 nm is 2.2%, the average transmittance in the wavelength range of 700 to 800 nm is 1.1%, the transmittance at a wavelength of 1100 nm is 1.2%, the IR cut-off wavelength is 680 nm, and the UV cut-off wavelength is 397 nm.

(ε3): When the incident angle of light is 40°, the transmittance at a wavelength of 380 nm is 13.1%, the transmittance at a wavelength of 40° nm is 90.5%, the average transmittance in the wavelength range of 450 to 600 nm is 92.1%, the lowest transmittance in the wavelength range of 450 to 600 nm is 87.6%, the transmittance at a wavelength of 700 nm is 2.0%, the transmittance at a wavelength of 715 nm is 0.8%, the average transmittance in the wavelength range of 700 to 800 nm is 0.5% or less, the transmittance at a wavelength of 1100 nm is 5.4%, the IR cut-off wavelength is 661 nm, and the UV cut-off wavelength is 386 nm.

A coating liquid IRA3 containing an infrared-absorbing dye was prepared in the following manner. The infrared-absorbing dye is a combination of a cyanine-based organic dye and squarylium-based organic dye and is soluble in MEK. The infrared-absorbing dye was added to MEK serving as a solvent, and PVB serving as a matrix was also added thereto, followed by stirring for 2 hours to obtain a coating liquid IRA3. The content of the matrix in the solids of the coating liquid IRA3 was 99 mass %. The coating liquid IRA3 was applied onto the other principal surface of the transparent glass substrate of the intermediate product ε by spin coating, and the resultant film was cured by heating at 140° C. for 30 minutes to form an infrared-absorbing layer ira3. Separately, an infrared-absorbing layer was formed on one principal surface of a transparent glass substrate (manufactured by SCHOTT AG, product name: D 263 T eco) under the same conditions as those for the formation of the infrared-absorbing layer ira3 to produce a laminate according to Reference Example 5. A transmittance spectrum shown by the laminate according to Reference Example 5 at an incident angle of 0° is shown in FIG. 15B. The laminate according to Reference Example 5 has the following characteristics (v1) to (v4).

(v1): The transmittance at a wavelength of 700 nm is 2.0%, the transmittance at a wavelength of 715 nm is 2.6%, and the average transmittance in the wavelength range of 700 to 800 nm is 15.9%.

(v2): The transmittance at a wavelength of 1100 nm is 91.1%.

(v3): The transmittance at a wavelength of 40° nm is 78.2%, the transmittance at a wavelength of 450 nm is 83.8%, and the average transmittance in the wavelength range of 500 to 600 nm is 86.9%.

(v4): The IR cut-off wavelength in the wavelength range of 600 nm to 700 nm is 637 nm, the IR cut-off wavelength in the wavelength range of 700 nm to 800 nm is 800 nm, the difference between these IR cut-off wavelengths is 163 nm, and the wavelength of maximum absorption in the wavelength range of 600 nm to 800 nm is 706 nm.

An anti-reflection film ar1 was formed on the infrared-absorbing layer ira3 using a vacuum deposition apparatus in the same manner as in Example 1 to obtain an optical filter according to Comparative Example 1.

Transmittance spectra of the optical filter according to Comparative Example 1 are shown in FIG. 15C and Table 45. The optical filter according to Comparative Example 1 has the characteristics shown in Table 46. A relationship between wavelengths and differences between spectral transmittances of the optical filter according to Comparative Example 1 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 16A. A relationship between wavelengths and the absolute values of the differences between spectral transmittances of the optical filter according to Comparative Example 1 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 16B. A relationship between wavelengths and the square values of the differences between spectral transmittances of the optical filter according to Comparative Example 1 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 16C. IE_(θ1/θ2) ^(λ1 to λ2), IAE_(θ1/θ2) ^(λ1 to λ2), and ISE_(θ1/θ2) ^(λ1 to λ2) were determined in the domain of the wavelength λ where λ1=350 and λ2=800, the domain of the wavelength λ where λ1=380 and λ2=530, the domain of the wavelength λ where λ1=450 and λ2=650, and the domain of the wavelength λ where λ1=530 and λ2=750. The results are shown in Tables 47 to 50.

Comparative Example 2

An infrared-absorbing glass substrate showing the transmittance spectrum shown in FIG. 17A at an incident angle of 0° was prepared. The infrared-absorbing glass substrate has the following characteristics (g1) to (g5).

(g1): The average transmittance in the wavelength range of 700 to 1000 nm is 16.8%.

(g2): The average transmittance in the wavelength range of 1100 to 1200 nm is 38.5%.

(g3): The average transmittance in the wavelength range of 450 to 600 nm is 87.8%.

(g4): The transmittance at a wavelength of 40° nm is 88.5%.

(g5): The IR cut-off wavelength is 653 nm. The wavelength which lies in the wavelength range of 600 to 800 nm and at which the transmittance is 20% is 738 nm.

An infrared-reflecting film irr3 was formed on one principal surface of the infrared-absorbing glass substrate, which has a thickness of 210 μm, by alternately laminating SiO₂ and TiO₂ in 20 layers using a vacuum deposition apparatus. An intermediate product was thus obtained. An infrared-reflecting film was formed on one principal surface of a transparent glass substrate (manufactured by SCHOTT AG, product name: D 263 T eco) under the same conditions as for the formation of the infrared-reflecting film irr3 to obtain a laminate according to Reference Example 6. Transmittance spectra of the laminate according to Reference Example 6 are shown in FIG. 17B. The laminate according to Reference Example 6 has the following characteristics (w1) to (w3).

(w1): When the incident angle of light is 0°, the transmittance at a wavelength of 380 nm is 0.5% or less, the transmittance at a wavelength of 40° nm is 0.5% or less, the average transmittance in the wavelength range of 450 to 600 nm is 95.2%, the lowest transmittance in the wavelength range of 450 to 600 nm is 93.7%, the average transmittance in the wavelength range of 700 to 800 nm is 4.7%, the transmittance at a wavelength of 1100 nm is 0.5% or less, the IR cut-off wavelength is 702 nm, and the UV cut-off wavelength is 411 nm.

(w2): When the incident angle of light is 30°, the transmittance at a wavelength of 380 nm is 1.7%, the transmittance at a wavelength of 40° nm is 77.7%, the average transmittance in the wavelength range of 450 to 600 nm is 94.1%, the lowest transmittance in the wavelength range of 450 to 600 nm is 93.0%, the average transmittance in the wavelength range of 700 to 800 nm is 1.1%, the transmittance at a wavelength of 1100 nm is 1.2%, the IR cut-off wavelength is 680 nm, and the UV cut-off wavelength is 397 nm.

(w3): When the incident angle of light is 40°, the transmittance at a wavelength of 380 nm is 13.1%, the transmittance at a wavelength of 40° nm is 90.5%, the average transmittance in the wavelength range of 450 to 600 nm is 92.1%, the lowest transmittance in the wavelength range of 450 to 600 nm is 87.6%, the average transmittance in the wavelength range of 700 to 800 nm is 0.5% or less, the transmittance at a wavelength of 1100 nm is 5.4%, the IR cut-off wavelength is 661 nm, and the UV cut-off wavelength is 386 nm.

A coating liquid UVIRA2 containing an infrared-absorbing dye and ultraviolet-absorbing dye was prepared in the following manner. The ultraviolet-absorbing dye is a dye composed of a benzophenone-based ultraviolet-absorbing substance which is less likely to absorb light in the visible region. The infrared-absorbing dye is a combination of a cyanine-based organic dye and squarylium-based organic dye. The infrared-absorbing dye and ultraviolet-absorbing dye are soluble in MEK. The infrared-absorbing dye and ultraviolet-absorbing dye were added to MEK serving as a solvent, and PVB serving as a matrix was also added thereto, followed by stirring for 2 hours to obtain a coating liquid UVIRA2. The content of PVB in the solids of the coating liquid UVIRA2 was 60 mass %. The coating liquid UVIRA2 was applied onto the other principal surface of the intermediate product, and the resultant film was cured by heating to form an infrared- and ultraviolet-absorbing layer uvira2. The thickness of the infrared- and ultraviolet-absorbing layer uvira2 is 7 μm. An infrared- and ultraviolet-absorbing layer was formed on one principal surface of a transparent glass substrate (manufactured by SCHOTT AG, product name: D 263 T eco) using the coating liquid UVIRA2 under the same conditions as those for the formation of the infrared- and ultraviolet-absorbing layer uvira2 to produce a laminate according to Reference Example 7. A transmittance spectrum shown by the laminate according to Reference Example 7 at an incident angle of 0° is shown in FIG. 17C. The laminate according to Reference Example 7 has the following characteristics (p1) to (p5).

(p1): The transmittance at a wavelength of 700 nm is 4.9%, the transmittance at a wavelength of 715 nm is 8.4%, and the average transmittance in the wavelength range of 700 to 800 nm is 63.9%.

(p2): The transmittance at a wavelength of 1100 nm is 92.3%.

(p3): The transmittance at a wavelength of 40° nm is 12.6%, the transmittance at a wavelength of 450 nm is 84.4%, and the average transmittance in the wavelength range of 500 to 600 nm is 88.7%.

(p4): The IR cut-off wavelength in the wavelength range of 600 nm to 700 nm is 664 nm, the IR cut-off wavelength in the wavelength range of 700 nm to 800 nm is 731 nm, and the difference therebetween is 67 nm. The wavelength (wavelength of maximum absorption) at which the transmittance is the lowest in the wavelength range of 600 nm to 800 nm is 705 nm.

(p5): The UV cut-off wavelength in the wavelength range of 350 nm to 450 nm is 411 nm.

In the same manner as in Example 1, an anti-reflection film ar1 was formed on the infrared- and ultraviolet-absorbing layer uvira2 using a vacuum deposition apparatus. The anti-reflection film ar1 is a film composed of SiO₂ and TiO₂ that are alternately laminated, includes 7 layers, and has a total thickness of about 0.4 μm. An optical filter according to Comparative Example 2 was thus obtained.

Transmittance spectra of the optical filter according to Comparative Example 2 are shown in FIG. 17D and Table 51. The optical filter according to Comparative Example 2 has the characteristics shown in Table 52. A relationship between wavelengths and differences between spectral transmittances of the optical filter according to Comparative Example 2 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 18A. A relationship between wavelengths and the absolute values of the differences between spectral transmittances of the optical filter according to Comparative Example 2 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 18B. A relationship between wavelengths and the square values of the differences between spectral transmittances of the optical filter according to Comparative Example 2 at two incident angles selected from 0°, 30°, and 40° is shown in FIG. 18C. IE_(θ1/θ2) ^(λ1 to λ2), IAE_(θ1/θ2) ^(λ1 to λ2), and ISE_(θ1/θ2) ^(λ1 to λ2) were determined in the domain of the wavelength λ where λ1=350 and λ2=800, the domain of the wavelength λ where 1=380 and λ2=530, the domain of the wavelength λ where λ1=450 and λ2=650, and the domain of the wavelength λ where λ1=530 and λ2=750. The results are shown in Tables 53 to 56.

The requirements (i) to (vii) are satisfied by the optical filters according to Examples 1 to 6. The optical filters according to Examples 1 to 6 have sufficiently low transmittances in the wavelength range of 700 nm or more, which indicates that the optical filters according to Examples 1 to 6 can shield against near-infrared light well. In the wavelength range of 700 nm or more, the optical filter according to Example 2 exhibits lower transmittances than those of the optical filter according to Example 1. Since the optical filter according to Example 2 includes the infrared-absorbing dye, the transmittances of the optical filter according to Example 2 are lower in the visible region than those of the optical filter according to Example 1 by about 2 points. This is, however, not considered problematic in practical use. The optical filter according to Example 3, which includes only the infrared-absorbing layer ira11 and infrared-absorbing layer ira12 as infrared-absorbing layers, exhibits higher transmittances in the wavelength range of 1100 nm or more than in the wavelength range of 700 to 1100 nm and than the transmittances of the optical filters according to Examples 1 and 2 in the wavelength range of 1100 nm or more. Nevertheless, the optical filter according to Example 3 is considered to have appropriate characteristics for imaging apparatuses because imaging devices such as CMOS sensors have a low sensitivity to light with a wavelength of 1100 nm or more. Although higher than the transmittances of the optical filters of other Examples at around a wavelength of 40° nm, the transmittance of the optical filter according to Example 6 at around a wavelength of 40° nm is 45% or less.

The requirements shown in Tables (I) to (IV) are satisfied by the optical filters according to Examples 1 to 6. In particular, the spectral transmittances of the optical filters according to Examples 1 to 3 and 6 do not vary between incident angles of 0°, 30°, and 40° in the domains of the wavelength A. Thus, for the optical filters according to Examples 1 to 3 and 6, the values of IE_(θ1/θ2) ^(λ1 to λ2) are sufficiently small with respect to the upper limits of IE_(θ1/θ2) ^(λ1 to λ2) in Tables (I) to (IV) and sufficiently large with respect to the lower limits in Tables (I) to (V). Additionally, for the optical filters according to Examples 1 to 3 and 6, the values of IAE_(θ1/θ2) ^(λ1 to λ2) and ISE_(θ1/θ2) ^(λ1 to λ2) in Table (I) are sufficiently small with respect to the upper limits of IAE_(θ1/θ2) ^(λ1 to λ2) and ISE_(θ1/θ2) ^(λ1 to λ2) in Tables (I) to (V). The infrared-reflecting films of the optical filters according to Examples 4 and 5 are configured so that the boundary between a wavelength band of light that is incident at an incident angle of 40° and is transmitted and a wavelength band of light that is incident at an incident angle of 40° and is reflected is around 850 nm. Thus, the spectral transmittances of the optical filters according to Examples 4 and 5 scarcely vary between incident angles of 0°, 30°, and 40° on the long wavelength side (the wavelength range of 600 nm to 800 nm) of the wavelength range of 350 nm to 800 nm. Meanwhile, the transmittances of the optical filters according to Examples 4 and 5 at around a wavelength of 40° nm are higher at a larger incident angle of light. The effect of this is seen in IE_(0/30) ^(380 to 530), IE_(0/40) ^(380 to 530), IAE_(0/30) ^(380 to 530), IAE_(0/40) ^(380 to 530), ISE_(0/30) ^(380 to 530), and ISE_(0/40) ^(380 to 530) of the optical filters according to Examples 4 and 5. At around a wavelength of 530 nm, the spectral transmittance of each of the optical filters according to Examples 4 and 5 at an incident angle of 30° is higher than the spectral transmittances of each of the optical filters according to Examples 4 and 5 at incident angles of 0° and 40°. The effect of this is seen in IE_(0/30) ^(450 to 650), IE_(30/40) ^(450 to 650), IAE_(0/30) ^(450 to 650), IAE_(0/40) ^(450 to 650), ISE_(0/30) ^(450 to 650), and ISE_(30/40) ^(450 to 650). However, these effects are so small that the requirements shown in Tables (I) to (IV) are satisfied. Therefore, it is thought that when each of the optical filters according to Examples 1 to 6 is incorporated in a camera module, incidence of light on the optical filter at an incident angle in the range of 0° to 40° does not cause uneven coloring of a taken image.

In a part of the visible region adjacent to the near-infrared region and the near-infrared region, the infrared-absorbing layer ira3 of the optical filter according to Comparative Example 1 determines the boundary between a light transmission wavelength band and a light shielding wavelength band. However, because of a narrow absorption band of the infrared-absorbing layer ira3, the transmittance spectrum of the optical filter according to Comparative Example 1 is affected more greatly by the effect of a shift of a reflection band of the infrared-reflecting film to the short wavelength side as the incident angle of light increases. Moreover, the optical filter according to Comparative Example 1, which has an insufficient ability to absorb light in the ultraviolet region, substantially uses the infrared-reflecting film irr2 alone to shield against light in the ultraviolet region. Thus, in the ultraviolet region, the optical filter according to Comparative Example 1 is strongly affected by the effect of the incident angle-dependent shift of the reflection band to the short wavelength side. Thus, although the optical filter according to Comparative Example 1 satisfies the requirements (i) to (vii), the spectral transmittance of the optical filter according to Comparative Example 1 at around 40° nm greatly varies between incident angles of 0° and 30°. Additionally, the spectral transmittance of the optical filter according to Comparative Example 1 at around 650 nm greatly varies between incident angles of 0° and 40°. Besides, the spectral transmittances of the optical filter according to Comparative Example 1 in the range of 450 nm to 650 nm locally and greatly vary between incident angles of 0° and 40° and incident angles of 30° and 40°. IAE_(30/40) ^(350 to 800), ISE_(30/40) ^(380 to 800), IAE_(30/40) ^(380 to 530), ISE_(30/40) ^(380 to 530), IE_(30/40) ^(450 to 650), IAE_(30/40) ^(450 to 650), IE_(30/40) ^(530 to 750), IAE_(30/40) ^(530 to 750), and ISE_(30/40) ^(530 to 750) do not fall under the ranges shown in Tables (I) to (IV). Therefore, there is concern that when the optical filter according to Comparative Example 1 is incorporated in an imaging apparatus, a narrow area of an image obtained using the imaging apparatus may be colored quite unevenly.

In a part of the visible region adjacent to the near-infrared region and the near-infrared region, and the ultraviolet region, the infrared- and ultraviolet-absorbing layer uvira2 of the optical filter according to Comparative Example 2 determines the boundary between a light transmission wavelength band and a light shielding wavelength band. However, because of a narrow absorption band of the infrared- and ultraviolet-absorbing layer uvira2 in the near-infrared region, the optical filter according to Comparative Example 2 shows a high value of IE_(30/40) ^(350 to 800). Additionally, a local variation (ripple) in spectral transmittance is observed in the visible region of the transmittance spectrum shown by the optical filter according to Comparative Example 2 at an incident angle of 40°. Therefore, IE_(30/40) ^(350 to 800), IAE_(30/40) ^(350 to 800), IE_(30/40) ^(380 to 530), IAE_(30/40) ^(380 to 530), IE_(30/40) ^(450 to 650), IAE_(30/40) ^(450 to 650), IE_(30/40) ^(530 to 750), and IAE_(30/40) ^(530 to 750) are particularly high. Therefore, there is concern that when the optical filter according to Comparative Example 2 is incorporated in an imaging apparatus, a narrow area of an image obtained using the imaging apparatus may be colored quite unevenly.

TABLE 9 Transmittance [%] Incident Incident Incident Wavelength angle angle angle [nm] θ = 0° θ = 30° θ = 40° 350 0.0 0.0 0.0 380 0.0 0.0 0.0 390 0.1 0.1 0.1 400 9.3 8.2 7.3 410 44.6 42.8 41.1 420 70.4 69.6 68.3 430 80.4 80.4 79.5 440 84.3 84.7 83.9 450 87.1 87.7 87.0 460 88.9 89.5 88.7 470 89.7 90.2 89.3 480 91.1 91.5 90.6 490 92.9 93.3 92.2 500 92.4 92.6 91.4 510 93.9 94.1 92.8 520 93.6 93.6 92.3 530 94.1 94.2 92.8 540 93.5 93.4 92.0 550 94.0 93.9 92.6 560 92.3 92.1 90.7 570 92.1 91.9 90.5 580 88.8 88.4 87.0 590 86.1 85.6 84.2 600 80.6 79.8 78.4 610 73.0 71.9 70.4 620 64.5 63.2 61.6 630 53.4 51.8 50.0 640 41.5 39.7 38.0 650 30.2 28.4 26.8 660 20.0 18.4 17.0 670 12.3 11.0 9.9 680 7.0 6.0 5.3 690 3.8 3.2 2.7 700 1.9 1.5 1.3 710 1.0 0.7 0.6 715 0.7 0.5 0.4 730 0.3 0.2 0.1 740 0.1 0.1 0.1 750 0.1 0.1 0.0 760 0.0 0.0 0.0 770 0.0 0.0 0.0 780 0.0 0.0 0.0 790 0.0 0.0 0.0 800 0.0 0.0 0.0 820 0.0 0.0 0.0 840 0.0 0.0 0.0 860 0.0 0.0 0.0 880 0.0 0.0 0.0 900 0.0 0.0 0.0 920 0.0 0.0 0.0 940 0.0 0.0 0.0 960 0.0 0.0 0.0 980 0.1 0.0 0.0 1000 0.1 0.1 0.0 1020 0.1 0.1 0.1 1040 0.2 0.1 0.1 1060 0.3 0.2 0.2 1080 0.5 0.4 0.3 1100 0.9 0.6 0.5 1120 1.4 1.0 0.8 1140 2.1 1.6 1.3 1160 3.2 2.6 2.2 1180 4.7 3.9 3.3 1200 6.6 5.6 4.9

TABLE 10 Average Average Average Average Full width at transmittance transmittance transmittance transmittance half in wavelength in wavelength in wavelength in wavelength IR cut-off UV cut-off maximum Incident range of 700 to range of 700 to range of 1100 range of 500 to wavelength wavelength transmission angle θ 800 nm [%] 1000 nm [%] to 1200 nm [%] 600 nm [%] [nm] [nm] region [nm]  0° 0.5 or less 0.5 or less 3.0 91.5 633 412 221 30° 0.5 or less 0.5 or less 2.4 91.4 631 412 219 40° 0.5 or less 0.5 or less 2.1 90.0 630 413 217

TABLE 11 IE_(0/30) ^(350 to 800) IE_(0/40) ^(350 to 800) IE_(30/40) ^(350 to 800) 1.56 5.29 3.73 IAE_(0/30) ^(350 to 800) IAE_(0/40) ^(350 to 800) IAE_(30/40) ^(350 to 800) 2.26 5.29 3.73 ISE_(0/30) ^(350 to 800) ISE_(0/40) ^(350 to 800) ISE_(30/40) ^(350 to 800) 0.03 0.12 0.05

TABLE 12 IE_(0/30) ^(380 to 530) IE_(0/40) ^(380 to 530) IE_(30/40) ^(380 to 530) 0.02 1.48 1.45 IAE_(0/30) ^(380 to 530) IAE_(0/40) ^(380 to 530) IAE_(30/40) ^(380 to 530) 0.72 1.48 1.45 ISE_(0/30) ^(380 to 530) ISE_(0/40) ^(380 to 530) ISE_(30/40) ^(380 to 530) 0.01 0.03 0.02

TABLE 13 IE_(0/30) ^(450 to 650) IE_(0/40) ^(450 to 650) IE_(30/40) ^(450 to 650) 0.63 3.28 2.65 IAE_(0/30) ^(450 to 650) IAE_(0/40) ^(450 to 650) IAE_(30/40) ^(450 to 650) 1.17 3.28 2.65 ISE_(0/30) ^(450 to 650) ISE_(0/40) ^(450 to 650) ISE_(30/40) ^(450 to 650) 0.01 0.07 0.04

TABLE 14 IE_(0/30) ^(530 to 750) IE_(0/40) ^(530 to 750) IE_(30/40) ^(530 to 750) 1.54 3.82 2.29 IAE_(0/30) ^(530 to 750) IAE_(0/40) ^(530 to 750) IAE_(30/40) ^(530 to 750) 1.54 3.82 2.29 ISE_(0/30) ^(530 to 750) ISE_(0/40) ^(530 to 750) ISE_(30/40) ^(530 to 750) 0.02 0.09 0.03

TABLE 15 Transmittance [%] Incident Incident Incident Wavelength angle angle angle [nm] θ = 0° θ = 30° θ = 40° 350 0.0 0.0 0.0 380 0.0 0.0 0.0 390 0.1 0.1 0.1 400 8.3 7.3 6.5 410 40.0 38.2 36.5 420 63.5 62.5 61.0 430 74.2 73.9 72.8 440 78.9 78.9 78.0 450 82.2 82.5 81.5 460 85.6 86.0 85.1 470 87.8 88.2 87.2 480 89.7 90.0 89.0 490 91.7 92.0 90.9 500 91.4 91.5 90.3 510 92.9 93.0 91.7 520 92.4 92.4 91.1 530 93.1 93.1 91.7 540 92.4 92.2 90.8 550 92.5 92.3 90.9 560 90.3 90.0 88.6 570 89.7 89.3 87.9 580 85.6 85.0 83.6 590 81.6 80.9 79.4 600 74.5 73.5 72.0 610 65.3 63.9 62.2 620 54.7 53.1 51.3 630 41.9 40.1 38.3 640 30.0 28.1 26.5 650 20.2 18.5 17.1 660 11.8 10.5 9.5 670 5.8 4.9 4.3 680 2.1 1.7 1.4 690 0.6 0.4 0.3 700 0.1 0.1 0.1 710 0.1 0.0 0.0 715 0.1 0.0 0.0 730 0.1 0.1 0.0 740 0.1 0.0 0.0 750 0.0 0.0 0.0 760 0.0 0.0 0.0 770 0.0 0.0 0.0 780 0.0 0.0 0.0 790 0.0 0.0 0.0 800 0.0 0.0 0.0 820 0.0 0.0 0.0 840 0.0 0.0 0.0 860 0.0 0.0 0.0 880 0.0 0.0 0.0 900 0.0 0.0 0.0 920 0.0 0.0 0.0 940 0.0 0.0 0.0 960 0.0 0.0 0.0 980 0.0 0.0 0.0 1000 0.1 0.0 0.0 1020 0.1 0.1 0.0 1040 0.1 0.1 0.1 1060 0.2 0.1 0.1 1080 0.3 0.2 0.2 1100 0.6 0.4 0.3 1120 0.9 0.7 0.6 1140 1.5 1.1 0.9 1160 2.3 1.8 1.5 1180 3.5 2.9 2.5 1200 5.2 4.3 3.7

TABLE 16 Average Average Average Average Full width transmittance transmittance transmittance transmittance at half in wavelength in wavelength in wavelength in wavelength IR cut-off UV cut-off maximum in Incident range of 700 to range of 700 to range of 1100 to range of 500 to wavelength wavelength transmission angle θ 800 nm [%] 1000 nm [%] 1200 nm [%] 600 nm [%] [nm] [nm] region [%]  0° 0.5 or less 0.5 or less 2.2 89.4 624 413 210 30° 0.5 or less 0.5 or less 1.8 89.0 622 414 208 40° 0.5 or less 0.5 or less 1.5 87.7 621 415 206

TABLE 17 IE_(0/30) ^(350 to 800) IE_(0/40) ^(350 to 800) IE_(30/40) ^(350 to 800) 1.69 5.36 3.67 IAE_(0/30) ^(350 to 800) IAE_(0/40) ^(350 to 800) IAE_(30/40) ^(350 to 800) 2.10 5.36 3.67 ISE_(0/30) ^(350 to 800) ISE_(0/40) ^(350 to 800) ISE_(30/40) ^(350 to 800) 0.03 0.12 0.05

TABLE 18 IE_(0/30) ^(380 to 530) IE_(0/40) ^(380 to 530) IE_(30/40) ^(380 to 530) 0.23 1.78 1.55 IAE_(0/30) ^(380 to 530) IAE_(0/40) ^(380 to 530) IAE_(30/40) ^(380 to 530) 0.63 1.78 1.55 ISE_(0/30) ^(380 to 530) ISE_(0/40) ^(380 to 530) ISE_(30/40) ^(380 to 530) 0.01 0.03 0.02

TABLE 19 IE_(0/30) ^(450 to 650) IE_(0/40) ^(450 to 650) IE_(30/40) ^(450 to 650) 0.92 3.67 2.75 IAE_(0/30) ^(450 to 650) IAE_(0/40) ^(450 to 650) IAE_(30/40) ^(450 to 650) 1.28 3.67 2.75 ISE_(0/30) ^(450 to 650) ISE_(0/40) ^(450 to 650) ISE_(30/40) ^(450 to 650) 0.02 0.09 0.04

TABLE 20 IE_(0/30) ^(530 to 750) IE_(0/40) ^(530 to 750) IE_(30/40) ^(530 to 750) 1.46 3.59 2.13 IAE_(0/30) ^(530 to 750) IAE_(0/40) ^(530 to 750) IAE_(30/40) ^(530 to 750) 1.46 3.59 2.13 ISE_(0/30) ^(530 to 750) ISE_(0/40) ^(530 to 750) ISE_(30/40) ^(530 to 750) 0.02 0.09 0.03

TABLE 21 Transmittance [%] Incident Incident Incident Wavelength angle angle angle [nm] θ = 0° θ = 30° θ = 40° 350 0.0 0.0 0.0 380 0.0 0.0 0.0 390 0.1 0.1 0.1 400 9.1 8.0 7.2 410 44.6 42.8 41.1 420 70.8 70.0 68.7 430 81.1 81.2 80.3 440 85.1 85.6 84.8 450 88.1 88.7 88.0 460 89.9 90.6 89.8 470 90.8 91.3 90.5 480 92.2 92.7 91.7 490 93.9 94.3 93.3 500 93.3 93.6 92.4 510 94.8 95.0 93.8 520 94.4 94.5 93.3 530 94.9 95.0 93.7 540 94.1 94.1 92.7 550 94.6 94.5 93.2 560 92.8 92.6 91.2 570 92.4 92.2 90.9 580 89.0 88.6 87.3 590 86.0 85.5 84.1 600 80.1 79.4 77.9 610 72.0 71.0 69.4 620 63.1 61.7 60.0 630 51.4 49.8 48.0 640 39.3 37.4 35.7 650 27.9 26.1 24.5 660 18.0 16.4 15.1 670 10.7 9.4 8.5 680 5.9 5.0 4.4 690 3.1 2.5 2.2 700 1.5 1.2 1.0 710 0.8 0.6 0.5 715 0.5 0.4 0.3 730 0.2 0.1 0.1 740 0.1 0.1 0.1 750 0.1 0.0 0.0 760 0.1 0.0 0.0 770 0.0 0.0 0.0 780 0.0 0.0 0.0 790 0.0 0.0 0.0 800 0.0 0.0 0.0 820 0.0 0.0 0.0 840 0.0 0.0 0.0 860 0.0 0.0 0.0 880 0.0 0.0 0.0 900 0.0 0.0 0.0 920 0.1 0.0 0.0 940 0.1 0.1 0.1 960 0.2 0.2 0.1 980 0.4 0.3 0.2 1000 0.6 0.4 0.3 1020 0.9 0.7 0.5 1040 1.4 1.1 0.9 1060 2.4 1.9 1.5 1080 4.1 3.3 2.8 1100 6.7 5.6 4.8 1120 10.2 8.8 7.8 1140 14.6 12.8 11.6 1160 19.8 17.8 16.3 1180 24.9 22.8 21.2 1200 30.0 27.9 26.2

TABLE 22 Average Average Average Average Full width transmittance transmittance transmittance transmittance at half in wavelength in wavelength in wavelength in wavelength IR cut-off UV cut-off maximum in Incident range of 700 to range of 700 to range of 1100 to range of 500 to wavelength wavelength transmission angle θ 800 nm [%] 1000 nm [%] 1200 nm [%] 600 nm [%] [nm] [nm] region [nm]  0° 0.5 or less 0.5 or less 17.5 92.0 631 412 219 30° 0.5 or less 0.5 or less 15.8 91.9 630 412 218 40° 0.5 or less 0.5 or less 14.4 90.5 629 413 216

TABLE 23 IE_(0/30) ^(350 to 800) IE_(0/40) ^(350 to 800) IE_(30/40) ^(350 to 800) 1.45 5.10 3.65 IAE_(0/30) ^(350 to 800) IAE_(0/40) ^(350 to 800) IAE_(30/40) ^(350 to 800) 2.27 5.10 3.65 ISE_(0/30) ^(350 to 800) ISE_(0/40) ^(350 to 800) ISE_(30/40) ^(350 to 800) 0.03 0.12 0.05

TABLE 24 IE_(0/30) ^(380 to 530) IE_(0/40) ^(380 to 530) IE_(30/40) ^(380 to 530) −0.04 1.38 1.42 IAE_(0/30) ^(380 to 530) IAE_(0/40) ^(380 to 530) IAE_(30/40) ^(380 to 530) 0.77 1.38 1.42 ISE_(0/30) ^(380 to 530) ISE_(0/40) ^(380 to 530) ISE_(30/40) ^(380 to 530) 0.01 0.03 0.02

TABLE 25 IE_(0/30) ^(450 to 650) IE_(0/40) ^(450 to 650) IE_(30/40) ^(450 to 650) 0.59 3.21 2.62 IAE_(0/30) ^(450 to 650) IAE_(0/40) ^(450 to 650) IAE_(30/40) ^(450 to 650) 1.23 3.21 2.62 ISE_(0/30) ^(450 to 650) ISE_(0/40) ^(450 to 650) ISE_(30/40) ^(450 to 650) 0.01 0.07 0.04

TABLE 26 IE_(0/30) ^(530 to 750) IE_(0/40) ^(530 to 750) IE_(30/40) ^(530 to 750) 1.49 3.73 2.24 IAE_(0/30) ^(530 to 750) IAE_(0/40) ^(530 to 750) IAE_(30/40) ^(530 to 750) 1.49 3.73 2.24 ISE_(0/30) ^(530 to 750) ISE_(0/40) ^(530 to 750) ISE_(30/40) ^(530 to 750) 0.02 0.09 0.03

TABLE 27 Transmittance [%] Incident Incident Incident Wavelength angle angle angle [nm] θ = 0° θ = 30° θ = 40° 350 0.0 0.0 0.0 380 0.0 0.0 0.0 390 0.0 0.0 0.0 400 0.7 5.8 7.0 410 23.0 41.7 40.0 420 69.6 68.7 69.4 430 78.5 82.4 80.6 440 84.8 86.4 85.2 450 88.9 89.2 88.8 460 89.7 91.4 90.3 470 90.2 92.0 91.0 480 91.6 93.3 92.5 490 93.5 95.3 93.6 500 93.1 94.7 91.8 510 94.4 96.0 92.9 520 93.3 95.7 92.8 530 93.1 96.3 93.9 540 92.4 95.5 93.6 550 93.3 95.8 94.6 560 92.0 94.0 92.8 570 91.9 93.8 92.3 580 89.0 90.4 88.3 590 86.5 87.0 84.7 600 81.1 80.6 78.6 610 73.2 71.9 70.5 620 64.1 62.8 61.6 630 52.3 51.3 49.9 640 40.2 39.2 37.4 650 29.0 27.8 25.9 660 19.0 17.7 16.1 670 11.6 10.4 9.2 680 6.6 5.6 4.9 690 3.5 2.9 2.5 700 1.8 1.4 1.2 710 0.9 0.7 0.6 715 0.6 0.5 0.4 730 0.3 0.2 0.1 740 0.2 0.1 0.1 750 0.1 0.1 0.0 760 0.1 0.0 0.0 770 0.0 0.0 0.0 780 0.0 0.0 0.0 790 0.0 0.0 0.0 800 0.0 0.0 0.0 820 0.0 0.0 0.0 840 0.0 0.0 0.0 860 0.0 0.0 0.0 880 0.0 0.0 0.0 900 0.0 0.0 0.0 920 0.0 0.0 0.0 940 0.0 0.0 0.0 960 0.0 0.0 0.0 980 0.0 0.0 0.0 1000 0.1 0.0 0.0 1020 0.1 0.0 0.0 1040 0.1 0.1 0.1 1060 0.1 0.1 0.1 1080 0.2 0.2 0.3 1100 0.4 0.4 0.6 1120 0.6 0.8 1.2 1140 1.0 1.4 2.3 1160 1.5 2.4 4.2 1180 2.3 4.0 7.4 1200 3.3 6.6 12.4

TABLE 28 Average Average Average Average Full width transmittance transmittance transmittance transmittance at half in wavelength in wavelength in wavelength in wavelength IR cut-off UV cut-off maximum in Incident range of 700 to range of 700 to range of 1100 to range of 500 to wavelength wavelength transmission angle θ 800 nm [%] 1000 nm [%] 1200 nm [%] 600 nm [%] [nm] [nm] region [nm]  0° 0.5 or less 0.5 or less 1.4 91.3 632 414 218 30° 0.5 or less 0.5 or less 2.4 93.3 631 413 218 40° 0.5 or less 0.5 or less 4.2 91.1 630 413 217

TABLE 29 IE_(0/30) ^(350 to 800) IE_(0/40) ^(350 to 800) IE_(30/40) ^(350 to 800) −4.42 0.01 4.43 IAE_(0/30) ^(350 to 800) IAE_(0/40) ^(350 to 800) IAE_(30/40) ^(350 to 800) 6.78 6.30 4.69 ISE_(0/30) ^(350 to 800) ISE_(0/40) ^(350 to 800) ISE_(30/40) ^(350 to 800) 0.44 0.38 0.09

TABLE 30 IE_(0/30) ^(380 to 530) IE_(0/40) ^(380 to 530) IE_(30/40) ^(380 to 530) −4.26 −2.38 1.87 IAE_(0/30) ^(380 to 530) IAE_(0/40) ^(380 to 530) IAE_(30/40) ^(380 to 530) 4.33 3.07 2.13 ISE_(0/30) ^(380 to 530) ISE_(0/40) ^(380 to 530) ISE_(30/40) ^(380 to 530) 0.40 0.31 0.04

TABLE 31 IE_(0/30) ^(450 to 650) IE_(0/40) ^(450 to 650) IE_(30/40) ^(450 to 650) −2.20 1.37 3.57 IAE_(0/30) ^(450 to 650) IAE_(0/40) ^(450 to 650) IAE_(30/40) ^(450 to 650) 3.35 2.71 3.57 ISE_(0/30) ^(450 to 650) ISE_(0/40) ^(450 to 650) ISE_(30/40) ^(450 to 650) 0.07 0.05 0.07

TABLE 32 IE_(0/30) ^(530 to 750) IE_(0/40) ^(530 to 750) IE_(30/40) ^(530 to 750) −0.20 2.37 2.58 IAE_(0/30) ^(530 to 750) IAE_(0/40) ^(530 to 750) IAE_(30/40) ^(530 to 750) 2.47 3.22 2.58 ISE_(0/30) ^(530 to 750) ISE_(0/40) ^(530 to 750) ISE_(30/40) ^(530 to 750) 0.04 0.07 0.04

TABLE 33 Transmittance [%] Incident Incident Incident Wavelength angle angle angle [nm] θ = 0° θ = 30° θ = 40° 350 0.0 0.0 0.0 380 0.0 0.0 0.0 390 0.0 0.0 0.0 400 0.7 5.4 6.4 410 21.0 37.9 36.3 420 63.7 62.6 62.9 430 73.3 76.6 74.6 440 80.1 81.2 79.9 450 84.5 84.6 84.0 460 87.1 88.5 87.3 470 88.9 90.5 89.4 480 90.7 92.3 91.4 490 92.6 94.4 92.7 500 92.5 94.0 91.2 510 93.7 95.2 92.1 520 92.4 94.8 91.8 530 92.4 95.5 93.0 540 91.5 94.6 92.7 550 92.0 94.4 93.1 560 90.3 92.2 91.0 570 89.9 91.7 90.1 580 86.3 87.5 85.3 590 82.8 83.2 80.8 600 76.2 75.4 73.3 610 67.0 65.5 63.9 620 56.2 54.7 53.3 630 43.1 41.7 40.3 640 31.0 29.8 28.1 650 21.2 20.0 18.4 660 12.8 11.6 10.4 670 6.4 5.5 4.8 680 2.5 2.0 1.7 690 0.7 0.5 0.4 700 0.2 0.1 0.1 710 0.1 0.1 0.0 715 0.1 0.1 0.1 730 0.2 0.1 0.1 740 0.1 0.1 0.1 750 0.1 0.1 0.0 760 0.1 0.0 0.0 770 0.1 0.0 0.0 780 0.0 0.0 0.0 790 0.0 0.0 0.0 800 0.0 0.0 0.0 820 0.0 0.0 0.0 840 0.0 0.0 0.0 860 0.0 0.0 0.0 880 0.0 0.0 0.0 900 0.0 0.0 0.0 920 0.0 0.0 0.0 940 0.0 0.0 0.0 960 0.0 0.0 0.0 980 0.0 0.0 0.0 1000 0.1 0.0 0.0 1020 0.1 0.0 0.0 1040 0.1 0.1 0.1 1060 0.1 0.1 0.1 1080 0.2 0.2 0.3 1100 0.4 0.4 0.6 1120 0.6 0.8 1.2 1140 1.0 1.4 2.3 1160 1.5 2.5 4.3 1180 2.3 4.1 7.5 1200 3.4 6.7 12.6

TABLE 34 Average Average Average Average Full width transmittance transmittance transmittance transmittance at half in wavelength in wavelength in wavelength in wavelength IR cut-off UV cut-off maximum in Incident range of 700 to range of 700 to range of 1100 to range of 500 to wavelength wavelength transmission angle θ 800 nm [%] 1000 nm [%] 1200 nm [%] 600 nm [%] [nm] [nm] region [nm]  0° 0.5 or less 0.5 or less 1.5 89.6 625 415 210 30° 0.5 or less 0.5 or less 2.4 91.4 624 414 210 40° 0.5 or less 0.5 or less 4.3 89.2 623 414 209

TABLE 35 IE_(0/30) ^(350 to 800) IE_(0/40) ^(350 to 800) IE_(30/40) ^(350 to 800) −3.97 0.41 4.38 IAE_(0/30) ^(350 to 800) IAE_(0/40) ^(350 to 800) IAE_(30/40) ^(350 to 800) 6.21 5.73 4.58 ISE_(0/30) ^(350 to 800) ISE_(0/40) ^(350 to 800) ISE_(30/40) ^(350 to 800) 0.37 0.32 0.09

TABLE 36 IE_(0/30) ^(380 to 530) IE_(0/40) ^(380 to 530) IE_(30/40) ^(380 to 530) −3.83 −1.85 1.97 IAE_(0/30) ^(380 to 530) IAE_(0/40) ^(380 to 530) IAE_(30/40) ^(380 to 530) 3.93 2.76 2.17 ISE_(0/30) ^(380 to 530) ISE_(0/40) ^(380 to 530) ISE_(30/40) ^(380 to 530) 0.33 0.25 0.05

TABLE 37 IE_(0/30) ^(450 to 650) IE_(0/40) ^(450 to 650) IE_(30/40) ^(450 to 650) −1.89 1.76 3.65 IAE_(0/30) ^(450 to 650) IAE_(0/40) ^(450 to 650) IAE_(30/40) ^(450 to 650) 3.31 2.83 3.65 ISE_(0/30) ^(450 to 650) ISE_(0/40) ^(450 to 650) ISE_(30/40) ^(450 to 650) 0.06 0.06 0.07

TABLE 38 IE_(0/30) ^(530 to 750) IE_(0/40) ^(530 to 750) IE_(30/40) ^(530 to 750) −0.18 2.25 2.43 IAE_(0/30) ^(530 to 750) IAE_(0/40) ^(530 to 750) IAE_(30/40) ^(530 to 750) 2.31 2.96 2.43 ISE_(0/30) ^(530 to 750) ISE_(0/40) ^(530 to 750) ISE_(30/40) ^(530 to 750) 0.04 0.07 0.04

TABLE 39 Transmittance [%] Incident Incident Incident Wavelength angle angle angle [nm] θ = 0° θ = 30° θ = 40° 350 0.0 0.0 0.0 380 1.1 1.0 0.8 390 16.4 15.3 14.2 400 44.9 43.4 41.6 410 63.7 62.5 60.9 420 71.9 71.2 69.9 430 76.2 76.0 74.9 440 79.0 79.0 78.1 450 81.5 81.7 80.8 460 83.2 83.5 82.5 470 85.9 86.1 85.1 480 88.0 88.3 87.2 490 89.9 90.1 88.9 500 90.8 90.9 89.7 510 91.5 91.5 90.2 520 92.5 92.5 91.2 530 92.2 92.1 90.7 540 92.3 92.1 90.7 550 91.9 91.7 90.2 560 90.3 90.0 88.5 570 87.8 87.3 85.8 580 83.6 82.9 81.4 590 77.1 76.1 74.5 600 67.8 66.5 64.8 610 56.3 54.7 52.9 620 43.0 41.1 39.3 630 29.8 27.9 26.3 640 18.1 16.4 15.2 650 9.4 8.2 7.4 660 4.2 3.5 3.0 670 1.6 1.3 1.0 680 0.5 0.4 0.3 690 0.1 0.1 0.1 700 0.0 0.0 0.0 710 0.0 0.0 0.0 715 0.0 0.0 0.0 730 0.0 0.0 0.0 740 0.0 0.0 0.0 750 0.0 0.0 0.0 760 0.0 0.0 0.0 770 0.0 0.0 0.0 780 0.0 0.0 0.0 790 0.0 0.0 0.0 800 0.0 0.0 0.0 820 0.0 0.0 0.0 840 0.0 0.0 0.0 860 0.0 0.0 0.0 880 0.0 0.0 0.0 900 0.0 0.0 0.0 920 0.0 0.0 0.0 940 0.0 0.0 0.0 960 0.0 0.0 0.0 980 0.0 0.0 0.0 1000 0.0 0.0 0.0 1020 0.0 0.0 0.0 1040 0.0 0.0 0.0 1060 0.0 0.0 0.0 1080 0.0 0.0 0.0 1100 0.0 0.0 0.0 1120 0.0 0.0 0.0 1140 0.1 0.0 0.0 1160 0.2 0.1 0.1 1180 0.4 0.3 0.2 1200 0.7 0.5 0.4

TABLE 40 Average Average Average Average Full width transmittance transmittance transmittance transmittance at half in wavelength in wavelength in wavelength in wavelength IR cut-off UV cut-off maximum in Incident range of 700 to range of 700 to range of 1100 to range of 500 to wavelength wavelength transmission angle θ 800 nm [%] 1000 nm [%] 1200 nm [%] 600 nm [%] [nm] [nm] region [nm]  0° 0.5 or less 0.5 or less 0.5 or less 87.8 615 402 213 30° 0.5 or less 0.5 or less 0.5 or less 87.5 614 403 211 40° 0.5 or less 0.5 or less 0.5 or less 86.1 612 404 208

TABLE 41 IE_(0/30) ^(350 to 800) IE_(0/40) ^(350 to 800) IE_(30/40) ^(350 to 800) 1.70 5.41 3.71 IAE_(0/30) ^(350 to 800) IAE_(0/40) ^(350 to 800) IAE_(30/40) ^(350 to 800) 1.98 5.41 3.71 ISE_(0/30) ^(350 to 800) ISE_(0/40) ^(350 to 800) ISE_(30/40) ^(350 to 800) 0.02 0.12 0.05

TABLE 42 IE_(0/30) ^(380 to 530) IE_(0/40) ^(380 to 530) IE_(30/40) ^(380 to 530) 0.35 2.11 1.76 IAE_(0/30) ^(380 to 530) IAE_(0/40) ^(380 to 530) IAE_(30/40) ^(380 to 530) 0.63 2.11 1.76 ISE_(0/30) ^(380 to 530) ISE_(0/40) ^(380 to 530) ISE_(30/40) ^(380 to 530) 0.01 0.04 0.02

TABLE 43 IE_(0/30) ^(450 to 650) IE_(0/40) ^(450 to 650) IE_(30/40) ^(450 to 650) 1.06 3.83 2.76 IAE_(0/30) ^(450 to 650) IAE_(0/40) ^(450 to 650) IAE_(30/40) ^(450 to 650) 1.31 3.83 2.76 ISE_(0/30) ^(450 to 650) ISE_(0/40) ^(450 to 650) ISE_(30/40) ^(450 to 650) 0.02 0.09 0.04

TABLE 44 IE_(0/30) ^(530 to 750) IE_(0/40) ^(530 to 750) IE_(30/40) ^(530 to 750) 1.35 3.31 1.96 IAE_(0/30) ^(530 to 750) IAE_(0/40) ^(530 to 750) IAE_(30/40) ^(530 to 750) 1.35 3.31 1.96 ISE_(0/30) ^(530 to 750) ISE_(0/40) ^(530 to 750) ISE_(30/40) ^(530 to 750) 0.02 0.09 0.03

TABLE 45 Transmittance [%] Incident Incident Incident Wavelength angle angle angle [nm] θ = 0° θ = 30° θ = 40° 350 2.4 0.3 0.3 380 0.3 1.6 11.8 390 0.9 8.0 67.3 400 2.7 68.8 79.4 410 43.3 81.2 64.9 420 81.8 79.2 63.5 430 81.4 81.1 81.1 440 82.4 86.1 83.2 450 88.4 89.4 84.5 460 91.5 91.5 91.1 470 93.2 95.0 91.4 480 95.2 96.1 93.1 490 93.8 96.2 93.0 500 95.3 96.8 89.8 510 95.7 96.5 90.9 520 93.5 95.4 94.1 530 92.9 95.7 92.7 540 92.5 95.7 91.7 550 91.7 93.7 92.5 560 91.5 92.2 91.7 570 90.6 90.9 88.8 580 88.4 88.4 86.2 590 85.7 84.9 84.0 600 81.7 80.8 79.8 610 75.8 75.1 73.3 620 68.0 67.1 65.3 630 59.3 57.9 56.1 640 51.1 49.4 44.9 650 43.4 41.5 29.2 660 34.4 32.0 16.7 670 23.0 17.9 6.3 680 11.7 5.6 1.2 690 4.8 1.0 0.2 700 1.9 0.1 0.0 710 1.0 0.1 0.0 715 0.9 0.1 0.0 730 0.8 0.1 0.0 740 0.5 0.1 0.0 750 0.2 0.1 0.0 760 0.1 0.0 0.0 770 0.1 0.0 0.0 780 0.1 0.0 0.0 790 0.1 0.0 0.1 800 0.1 0.1 0.1 820 0.1 0.1 0.2 840 0.1 0.1 0.3 860 0.1 0.2 0.6 880 0.1 0.3 0.9 900 0.2 0.5 0.7 920 0.3 0.5 0.5 940 0.4 0.4 0.4 960 0.4 0.3 0.4 980 0.4 0.3 0.4 1000 0.3 0.3 0.5 1020 0.2 0.3 0.6 1040 0.2 0.4 0.9 1060 0.2 0.5 1.5 1080 0.3 0.7 2.7 1100 0.4 1.2 5.4 1120 0.5 2.1 11.4 1140 0.7 4.1 21.5 1160 1.2 8.8 30.3 1180 2.1 18.9 36.3 1200 4.1 32.6 45.5

TABLE 46 Average Average Average Average Full width transmittance transmittance transmittance transmittance at half in wavelength in wavelength in wavelength in wavelength IR cut-off UV cut-off maximum in Incident range of 700 to range of 700 to range of 1100 to range of 500 to wavelength wavelength transmission angle θ 800 nm [%] 1000 nm [%] 1200 nm [%] 600 nm [%] [nm] [nm] region [nm]  0° 0.5 or less 0.5 or less  1.3 91.1 641 411 230 30° 0.5 or less 0.5 or less 10.0 92.2 639 398 241 40° 0.5 or less 0.5 or less 24.9 89.7 636 387 249

TABLE 47 IE_(0/30) ^(350 to 800) IE_(0/40) ^(350 to 800) IE_(30/40) ^(350 to 800) −9.30 −4.65 4.65 IAE_(0/30) ^(350 to 800) IAE_(0/40) ^(350 to 800) IAE_(30/40) ^(350 to 800) 17.10 32.43 22.35 ISE_(0/30) ^(350 to 800) ISE_(0/40) ^(350 to 800) ISE_(30/40) ^(350 to 800) 6.08 12.83 5.22

TABLE 48 IE_(0/30) ^(380 to 530) IE_(0/40) ^(380 to 530) IE_(30/40) ^(380 to 530) −12.04 −13.72 −1.68 IAE_(0/30) ^(380 to 530) IAE_(0/40) ^(380 to 530) IAE_(30/40) ^(380 to 530) 12.62 22.03 15.05 ISE_(0/30) ^(380 to 530) ISE_(0/40) ^(380 to 530) ISE_(30/40) ^(380 to 530) 5.91 11.74 4.59

TABLE 49 IE_(0/30) ^(450 to 650) IE_(0/40) ^(450 to 650) IE_(30/40) ^(450 to 650) −1.11 4.60 5.70 IAE_(0/30) ^(450 to 650) IAE_(0/40) ^(450 to 650) IAE_(30/40) ^(450 to 650) 2.63 4.95 5.70 ISE_(0/30) ^(450 to 650) ISE_(0/40) ^(450 to 650) ISE_(30/40) ^(450 to 650) 0.05 0.24 0.26

TABLE 50 IE_(0/30) ^(530 to 750) IE_(0/40) ^(530 to 750) IE_(30/40) ^(530 to 750) 2.28 9.12 6.85 IAE_(0/30) ^(530 to 750) IAE_(0/40) ^(530 to 750) IAE_(30/40) ^(530 to 750) 3.85 9.33 6.85 ISE_(0/30) ^(530 to 750) ISE_(0/40) ^(530 to 750) ISE_(30/40) ^(530 to 750) 0.12 1.01 0.61

TABLE 51 Transmittance [%] Incident Incident Incident Wavelength angle angle angle [nm] θ = 0° θ = 30° θ = 40° 350 0.0 0.0 0.0 380 0.0 0.0 0.0 390 0.0 0.0 0.2 400 0.0 9.6 10.1 410 16.1 47.0 36.7 420 67.6 69.3 55.2 430 79.9 78.7 78.6 440 84.8 84.9 82.0 450 86.6 88.2 83.3 460 90.9 90.4 89.9 470 91.7 92.7 89.2 480 91.9 93.7 90.7 490 95.0 94.3 91.2 500 93.3 94.0 87.1 510 94.2 94.8 89.2 520 93.7 92.7 91.4 530 94.6 93.8 90.9 540 92.4 92.8 88.8 550 91.2 91.0 89.7 560 88.9 88.1 87.5 570 88.0 87.2 85.0 580 83.0 82.5 80.3 590 78.6 78.0 77.0 600 73.0 72.1 70.9 610 66.6 65.4 63.4 620 59.9 58.2 56.2 630 50.4 48.8 47.0 640 42.7 40.8 36.8 650 35.8 34.6 24.1 660 28.6 26.9 13.9 670 20.4 15.8 5.5 680 11.2 5.5 1.1 690 4.5 0.9 0.2 700 1.5 0.1 0.0 710 0.8 0.0 0.0 715 0.5 0.0 0.0 730 0.2 0.1 0.0 740 0.1 0.1 0.0 750 0.0 0.1 0.0 760 0.0 0.0 0.0 770 0.0 0.0 0.0 780 0.0 0.0 0.0 790 0.0 0.0 0.0 800 0.0 0.0 0.0 820 0.0 0.0 0.0 840 0.0 0.0 0.0 860 0.0 0.0 0.1 880 0.0 0.0 0.1 900 0.0 0.1 0.1 920 0.0 0.1 0.1 940 0.0 0.1 0.1 960 0.0 0.1 0.1 980 0.0 0.1 0.1 1000 0.0 0.1 0.1 1020 0.0 0.1 0.1 1040 0.0 0.1 0.2 1060 0.0 0.1 0.4 1080 0.0 0.2 0.7 1100 0.0 0.3 1.4 1120 0.0 0.6 3.2 1140 0.0 1.3 6.7 1160 0.0 3.0 10.5 1180 0.0 7.1 13.7 1200 0.4 13.4 18.7

TABLE 52 Average Average Average Average Full width transmittance transmittance transmittance transmittance at half in wavelength in wavelength in wavelength in wavelength IR cut-off UV cut-off maximum in Incident range of 700 to range of 700 to range of 1100 to range of 500 to wavelength wavelength transmission angle θ 800 nm [%] 1000 nm [%] 1200 nm [%] 600 nm [%] [nm] [nm] region [nm]  0° 0.5 or less 0.5 or less 0.5 or less 88.8 630 414 216 30° 0.5 or less 0.5 or less 3.7 88.4 629 411 218 40° 0.5 or less 0.5 or less 8.8 85.9 627 417 210

TABLE 53 IE_(0/30) ^(350 to 800) IE_(0/40) ^(350 to 800) IE_(30/40) ^(350 to 800) −1.07 10.93 12.00 IAE_(0/30) ^(350 to 800) IAE_(0/40) ^(350 to 800) IAE_(30/40) ^(350 to 800) 7.63 16.46 12.33 ISE_(0/30) ^(350 to 800) ISE_(0/40) ^(350 to 800) ISE_(30/40) ^(350 to 800) 1.02 1.63 0.91

TABLE 54 IE_(0/30) ^(380 to 530) IE_(0/40) ^(380 to 530) IE_(30/40) ^(380 to 530) −3.95 1.75 5.70 IAE_(0/30) ^(380 to 530) IAE_(0/40) ^(380 to 530) IAE_(30/40) ^(380 to 530) 4.66 7.26 6.02 ISE_(0/30) ^(380 to 530) ISE_(0/40) ^(380 to 530) ISE_(30/40) ^(380 to 530) 0.93 0.81 0.45

TABLE 55 IE_(0/30) ^(450 to 650) IE_(0/40) ^(450 to 650) IE_(30/40) ^(450 to 650) 0.85 6.53 5.68 IAE_(0/30) ^(450 to 650) IAE_(0/40) ^(450 to 650) IAE_(30/40) ^(450 to 650) 1.71 6.53 5.68 ISE_(0/30) ^(450 to 650) ISE_(0/40) ^(450 to 650) ISE_(30/40) ^(450 to 650) 0.02 0.28 0.23

TABLE 56 IE_(0/30) ^(530 to 750) IE_(0/40) ^(530 to 750) IE_(30/40) ^(530 to 750) 2.90 9.23 6.33 IAE_(0/30) ^(530 to 750) IAE_(0/40) ^(530 to 750) IAE_(30/40) ^(530 to 750) 2.97 9.23 6.33 ISE_(0/30) ^(530 to 750) ISE_(0/40) ^(530 to 750) ISE_(30/40) ^(530 to 750) 0.09 0.81 0.47 

The invention claimed is:
 1. An optical filter comprising: a transparent substrate having a first side and a second side opposite to the first side; a first layer including a first light absorber including a copper ion and a first phosphonic acid with an aryl group; and at least one layer selected from the group consisting of a second layer including an ultraviolet absorber, a third layer including a second light absorber including a copper ion and a second phosphonic acid with an alkyl group, and a fourth layer including a dielectric multilayer film capable of reflecting at least a part of infrared light, the optical filter comprising one of the following layer structures (1), (2), (3) and (4): (1) the first layer and the third layer provided in sequence from the first side of the substrate, the first layer, and the third layer and the second layer provided in sequence from the second side of the substrate, (2) the first layer and the second layer provided in sequence from the first side of the substrate, and the first layer provided on the second side of the substrate, (3) the first layer and the fourth layer provided in sequence from the first side of the substrate, and the first layer and the second layer provided in sequence from the second side of the substrate, (4) the first layer and the third layer provided in sequence from the first side of the substrate, and the first layer and the third layer provided in sequence from the second side of the substrate, the optical filter, at each incident angle of 0°, 30°, and 40°, having: (i) a spectral transmittance of 3% or less at a wavelength of 700 nm; (ii) a spectral transmittance of 1% or less at a wavelength of 715 nm; (iii) a spectral transmittance of 7.5% or less at a wavelength of 1100 nm; (iv) an average transmittance of 1% or less at a wavelength range of 700 nm to 800 nm; (v) an average transmittance of 85% or more at a wavelength range of 500 nm to 600 nm; (vi) a spectral transmittance of 45% or less at a wavelength of 400 nm; and (vii) a spectral transmittance of 80% or more at a wavelength of 450 nm.
 2. The optical filter according to claim 1, further comprising an anti-reflection film, the anti-reflection film being disposed on the layer structures (1), (2), (3), or (4), on the farthest layer from the substrate.
 3. The optical filter according to claim 1, further comprising at least one fifth layer including SiO₂ between two layers selected from the group consisting of the first layer, the second layer, the third layer, and the fourth layer.
 4. The optical filter according to claim 1, wherein when the spectral transmittance of the optical filter at a wavelength λ and an incident angle θ° is expressed as T_(θ)(λ), the minimum and the maximum values of a domain of the wavelength λ are respectively expressed as λ1 and λ2, and the wavelength λ, is expressed as λ(n)=Δλ×n+λ1)[nm](Δλ=1) as a function of an integer n of 0 or more, IE_(θ1/θ2) ^(λ1 to λ2)defined by the following equation (1) for two incident angles θ1° and θ2° (θ1<θ2) selected from 0°, 30°, and 40° satisfy requirements shown in the following Table (I) for a domain of the wavelength λ where λ1=350 and λ2=800, a domain of the wavelength λ, where λ1=380 and λ2=530, a domain of the wavelength λ, where λ1=450 and λ2=650, and a domain of the wavelength λ, where λ1=530 and λ2=750: $\begin{matrix} {{IE}_{\theta 1/\theta 2}^{\lambda 1{to}\lambda 2} = {\sum\limits_{n = 0}^{{({{\lambda 2} - {\lambda 1}})}/\Delta\lambda}{\left\{ {{T_{\theta 1}\left( {\lambda(n)} \right)} - {T_{\theta 2}\left( {\lambda(n)} \right)}} \right\} \times \Delta\lambda}}} & (1) \end{matrix}$ TABLE I IE_(0/30) ^(350 to 800) IE_(0/40) ^(350 to 800) IE_(30/40) ^(350 to 800) −10 to 10 −14 to 14 −7 to 7 IE_(0/30) ^(380 to 530) IE_(0/40) ^(380 to 530) IE_(30/40) ^(380 to 530) −7 to 7 −10 to 10 −5 to 5 IE_(0/30) ^(450 to 650) IE_(0/40) ^(450 to 650) IE_(30/40) ^(450 to 650) −7 to 7 −10 to 10 −5 to 5 IE_(0/30) ^(530 to 750) IE_(0/40) ^(530 to 750) IE_(30/40) ^(530 to 750) −7 to 7 −10 to 10 −5 to 5


5. The optical filter according to claim 4, wherein IAE_(θ1/θ2) ^(λ1 to λ2)defined by the following equation (2) for two incident angles θ1° and θ2° (θ1<θ2) selected from 0°, 30°, and 40° satisfy requirements shown in the following Table (II) for a domain of the wavelength λ where λ1=350 and λ2=800, a domain of the wavelength λ, where λ1=380 and λ2=530, a domain of the wavelength λ where λ1=450 and λ2=650, and a domain of the wavelength λ, where λ1=530 and λ2=750: $\begin{matrix} {{IAE}_{\theta 1/\theta 2}^{\lambda 1{to}\lambda 2} = {\sum\limits_{n = 0}^{{({{\lambda 2} - {\lambda 1}})}/\Delta\lambda}{{❘{{T_{\theta 1}\left( {\lambda(n)} \right)} - {T_{\theta 2}\left( {\lambda(n)} \right)}}❘} \times \Delta\lambda}}} & (2) \end{matrix}$ TABLE II IAE_(0/30) ^(350 to 800) IAE_(0/40) ^(350 to 800) IAE_(30/40) ^(350 to 800) 0 to 7 0 to 10 0 to 7 IAE_(0/30) ^(380 to 530) IAE_(0/40) ^(380 to 530) IAE_(30/40) ^(380 to 530) 0 to 7 0 to 10 0 to 5 IAE_(0/30) ^(450 to 650) IAE_(0/40) ^(450 to 650) IAE_(30/40) ^(450 to 650) 0 to 7 0 to 10 0 to 5 IAE_(0/30) ^(530 to 750) IAE_(0/40) ^(530 to 750) IAE_(30/40) ^(530 to 750) 0 to 7 0 to 10 0 to 5


6. The optical filter according to claim 5, wherein ISE_(θ1/θ2) ^(λ1 to λ2)defined by the following equation (3) for two incident angles θ1° and θ2° (θ1<θ2) selected from 0°, 30°, and 40° satisfy requirements shown in the following Table (III) for a domain of the wavelength λ where λ1=350 and λ2=800, a domain of the wavelength λ where λ1=380 and λ2=530, a domain of the wavelength λ where λ1=450 and λ2=650, and a domain of the wavelength λ where λ1=530 and λ2=750: $\begin{matrix} {{ISE}_{\theta 1/\theta 2}^{\lambda 1{to}\lambda 2} = {\sum\limits_{n = 0}^{{({{\lambda 2} - {\lambda 1}})}/\Delta\lambda}{\left\{ {{T_{\theta 1}\left( {\lambda(n)} \right)} - {T_{\theta 2}\left( {\lambda(n)} \right)}} \right\}^{2} \times \Delta\lambda}}} & (3) \end{matrix}$ TABLE III ISE_(0/30) ^(350 to 800) ISE_(0/40) ^(350 to 800) ISE_(30/40) ^(350 to 800) 0 to 7    0 to 10 0 to 7   ISE_(0/30) ^(380 to 530) ISE_(0/40) ^(380 to 530) ISE_(30/40) ^(380 to 530) 0 to 0.7 0 to 1 0 to 0.5 ISE_(0/30) ^(450 to 650) ISE_(0/40) ^(450 to 650) ISE_(30/40) ^(450 to 650) 0 to 0.7 0 to 1 0 to 0.5 ISE_(0/30) ^(530 to 750) ISE_(0/40) ^(530 to 750) ISE_(30/40) ^(530 to 750) 0 to 0.7 0 to 1 0 to 0.5 